Method, system, device and medium for evaluating multi-dimensional time sequence similarity perceived by human eyes

Abstract

The present application relates to the field of industrial data processing, and particularly relates to a human eye perceived multi-dimensional time sequence similarity evaluation method, system, device and medium, the method comprising: processing a real value sequence and a predicted value sequence to generate a mapping sequence pair; extracting waveform geometric features of the mapping sequence pair to obtain a global shape similarity; performing exponential mapping on a cumulative cost of a nonlinear regular path using fluctuation scales of the mapping sequence pair to obtain a time regularity similarity; extracting local extreme points in the mapping sequence pair as feature anchor points, and obtaining a feature matching score based on offset distances of the mutually matched feature anchor points; extracting statistical moment features and statistical distribution evolution components of the mapping sequence pair to obtain a global distribution similarity; and finally performing multi-dimensional feature fusion to obtain a comprehensive evaluation score. Thus, the present application reconstructs a multi-dimensional evaluation system when a professional observes time sequence data from four dimensions of macro profile, phase alignment, key events and distribution density.

Description

Technical Field

[0001] This invention relates to the field of industrial data processing technology, and in particular to a method, system, device and medium for evaluating multidimensional temporal similarity perceived by the human eye. Background Technology

[0002] In the field of chemical process monitoring and optimization, real-time analysis and similarity evaluation of time-series data (such as core process parameters like temperature, pressure, flow rate, and liquid level) are core technical means to ensure production safety, provide early warning of abnormal operating conditions, and evaluate the effectiveness of control algorithms. Typically, by calculating the degree of matching between real-time curves collected on-site and ideal operating condition curves or historical high-quality operating condition prediction curves, the deviation characteristics of the production process can be quantified, thus providing a basis for process decision-making.

[0003] Currently, the industrial sector widely adopts mean square error (MSE). Mean absolute error ( Traditional numerical statistical indicators such as Euclidean distance are used as benchmarks for similarity evaluation. However, since these indicators are mainly calculated based on the absolute numerical differences between discrete sampling points, their evaluation logic relies too heavily on strict alignment at specific time points. In complex chemical production processes, due to measurement noise, time delay effects, and system inertia, time-series signals often exhibit phase shifts, amplitude scaling, and nonlinear local morphological fluctuations.

[0004] Traditional similarity evaluation systems focus on point-by-point comparison of static values, lacking the ability to comprehensively represent the macroscopic evolution trend and local structural features of signals. This makes it difficult for existing indicators to effectively distinguish waveform differences with similar numerical values ​​but vastly different physical meanings when faced with chemical parameters exhibiting strong nonlinearity and time-varying characteristics. Therefore, in practical applications, situations often arise where calculated similarity is high, but engineers identify significant differences in morphological features through visual observation. This severe deviation between evaluation results and human visual perception makes it difficult for existing indicator systems to comprehensively and objectively reflect the true matching state of the operating conditions, thus limiting the effectiveness of predictive models in complex process optimization and intelligent fault diagnosis. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] In view of the above-mentioned shortcomings and deficiencies of the prior art, the present invention provides a method, system, device and medium for evaluating multidimensional temporal similarity perceived by the human eye. It solves the technical problem that traditional evaluation indicators, which focus on static numerical comparison, are unable to capture the macroscopic evolution trend and local structural features of signals, resulting in a serious mismatch between the evaluation results and human visual perception, and are unable to accurately reflect the true matching state of complex chemical working conditions.

[0007] (II) Technical Solution

[0008] To achieve the above objectives, the main technical solutions adopted by the present invention include:

[0009] In a first aspect, embodiments of the present invention provide a method for evaluating multidimensional temporal similarity perceived by the human eye, comprising:

[0010] Obtain the true value sequence and predicted value sequence to be evaluated, and perform benchmark alignment and fluctuation amplitude normalization to generate corresponding mapping sequence pairs under a unified observation field;

[0011] The sampling window is used to extract the waveform geometric features of the mapping sequence pairs in the local interval, and the global morphological similarity is obtained based on the correlation strength of the waveform geometric features in the spatial dimension.

[0012] Nonlinear warping paths are established for mapping sequence pairs, and exponential mapping is performed on the cumulative cost generated by the path using the fluctuation scale of the mapping sequence pairs to obtain time warping similarity.

[0013] Local extreme points of each sequence in the mapping sequence pair are extracted as feature anchors, and feature matching scores are obtained based on the offset distance of the mutually matching feature anchors in the time and amplitude dimensions of the mapping sequence pair.

[0014] Extract the statistical moment features and statistical distribution evolution components of the mapped sequence pairs, and quantify the distribution consistency of the mapped sequence pairs in terms of statistical moment features and statistical distribution evolution components to obtain the global distribution similarity;

[0015] The global morphological similarity, temporal regularity similarity, feature matching score, and global distribution similarity are fused into a multi-dimensional feature to obtain a comprehensive evaluation score.

[0016] Optionally, the true value sequence and predicted value sequence to be evaluated are obtained, and benchmark alignment and fluctuation amplitude normalization are performed to generate corresponding mapping sequence pairs under a unified observation field, including:

[0017] Acquire a sequence of real values ​​consisting of at least one of the following: real-time data collected by physical sensors at the industrial site, historical observation records, or standard benchmark data; and a sequence of predicted values ​​generated by a preset time-series algorithm model.

[0018] Calculate the first mean and first standard deviation corresponding to the true value sequence, and the second mean and second standard deviation corresponding to the predicted value sequence, respectively;

[0019] The first centered sequence is obtained by subtracting the true value sequence using the first mean, and the second centered sequence is obtained by subtracting the predicted value sequence using the second mean, so as to align the waveform mean of each sequence to the zero-level reference and achieve reference alignment.

[0020] A numerical stability constant is introduced to avoid the division-to-zero anomaly. The first fluctuation scaling factor is obtained by summing the first standard deviation with the numerical stability constant, and the second fluctuation scaling factor is obtained by summing the second standard deviation with the numerical stability constant.

[0021] The first centering sequence is divided using the first fluctuation scaling factor to obtain the mapped true value sequence, and the second centering sequence is divided using the second fluctuation scaling factor to obtain the mapped predicted value sequence. The mapped true value sequence and the mapped predicted value sequence constitute a mapped sequence pair under a unified observation field.

[0022] Optionally, the waveform geometric features of the mapped sequence pairs within a local interval are extracted using a sampling window, and global morphological similarity is obtained based on the correlation strength of the waveform geometric features in the spatial dimension, including:

[0023] The dynamic range is determined based on the maximum and minimum values ​​of the mapped true value sequence and the numerical stability constant. The dynamic range is proportionally mapped using preset coefficients, and the mapping result is subjected to power transformation and numerical bias processing to obtain the first smoothing factor and the second smoothing factor.

[0024] A sliding traversal is performed along the time axis of the mapping sequence pairs using a preset sampling window to extract the corresponding local sequence of the true mapping value and the local sequence of the predicted mapping value at each sampling position.

[0025] Calculate the waveform geometric features corresponding to each sampling position. The waveform geometric features include the local mean and local standard deviation of the local sequence of the mapped true value and the local sequence of the mapped predicted value, as well as the local covariance between the local sequence of the mapped true value and the local sequence of the mapped predicted value.

[0026] Using the first and second smoothing factors, the local mean, local standard deviation and local covariance are multiplied and ratioed to obtain the local structural similarity index corresponding to the current sampling position.

[0027] The arithmetic mean of all local structural similarity indices generated during the sliding traversal is performed to obtain the global morphological similarity that characterizes the overall contour consistency of the waveform.

[0028] Optionally, a nonlinear warping path is established for the mapped sequence pair, and an exponential mapping is performed on the cumulative cost generated by the path using the fluctuation scale of the mapped sequence pair to obtain time-warped similarity, including:

[0029] The absolute numerical difference between the mapped true value sequence and the mapped predicted value sequence is calculated point by point, and a local distance matrix is ​​constructed to store the point-to-point metric cost.

[0030] Based on the length of the mapping sequence pairs, a cumulative distance matrix is ​​constructed to store the cumulative values ​​of the paths. An initialization process, including zeroing the starting position and defining the boundary maxima, is performed on the cumulative distance matrix to establish the boundary guiding constraints for the nonlinear regular path search.

[0031] Within the boundary guidance constraints and the search range determined by the preset window radius, the cumulative distance matrix is ​​cumulatively superimposed based on the local distance matrix and the cost recursive optimization logic to generate the minimum cumulative cost matrix from the start position of the sequence to each corresponding position, and the minimum cumulative cost matrix is ​​used to establish a nonlinear regularized path between the mapping sequence pairs.

[0032] Extract the value corresponding to the end position of the minimum cumulative cost matrix as the total cumulative cost generated by the nonlinear regularization path;

[0033] The fluctuation scale factor is determined based on the length, standard deviation and numerical stability constant of the mapped true value sequence, and the normalized path weight is obtained by performing a ratio operation between the total cumulative cost and the fluctuation scale factor.

[0034] Exponential mapping is used to transform the negative values ​​of normalized path weights into time regularization similarity, which represents the degree of time axis alignment between sequences.

[0035] Optionally, local extrema of each sequence in the mapped sequence pair are extracted as feature anchors, and feature matching scores are obtained based on the offset distances of the matching feature anchors in the time and magnitude dimensions of the mapped sequence pair, including:

[0036] Local extremum retrieval is performed on the mapping true value sequence and the mapping predicted value sequence according to the significance threshold determined by the standard deviation of the mapping true value sequence. The retrieved local maxima points are sorted in descending order according to the magnitude significance and a preset number of feature anchor points are retained to obtain the mapping true value feature anchor point set and the mapping predicted value feature anchor point set.

[0037] For each true value feature anchor in the set of true value feature anchors, the nearest neighbor search algorithm is used to match the corresponding associated anchor in the set of predicted value feature anchors, and the time offset between the true value feature anchor and the matched predicted value feature anchor is calculated.

[0038] Determine whether the time offset exceeds the maximum lag determined by the length of the mapped true value sequence;

[0039] If the time offset exceeds the maximum lag, the local matching component corresponding to the current true value feature anchor point will be set to zero.

[0040] If the time offset does not exceed the maximum lag, the position offset distance and amplitude deviation distance between the true value feature anchor point and the matched mapped predicted value feature anchor point are calculated. Then, using the position decay scale and amplitude decay scale determined based on the length and standard deviation of the mapped true value sequence, exponential decay mapping is performed on the position offset distance and amplitude deviation distance to obtain the corresponding local matching component.

[0041] For each true value feature anchor point, perform an arithmetic mean on all the local matching components to obtain the feature matching score that represents the degree of alignment of the mapping sequence pair at the morphological features.

[0042] Optionally, the statistical moment features and statistical distribution evolution components of the mapped sequence pairs are extracted, and the distributional consistency between the mapped sequence pairs in terms of statistical moment features and statistical distribution evolution components is quantified to obtain global distributional similarity, including:

[0043] For the mapped true value sequence and the mapped predicted value sequence, multi-order statistical moment features including mean, standard deviation, skewness and kurtosis are extracted respectively, and corresponding statistical moment feature vectors are constructed using the multi-order statistical moment features respectively;

[0044] The relative difference between each feature component of the statistical moment eigenvectors of the mapped true value sequence and the mapped predicted value sequence is calculated, and the mean of the relative difference is nonlinearly transformed using negative exponential mapping to obtain the statistical feature similarity.

[0045] According to the preset number of bins, the numerical histograms of the mapped true value sequence and the mapped predicted value sequence are statistically analyzed, and normalization is performed to obtain the statistical distribution evolution components that characterize the numerical density features of the sequence.

[0046] Calculate the distribution divergence index between the statistical distribution evolution components of the mapped true value sequence and the mapped predicted value sequence, and perform exponential mapping processing based on a preset scaling factor on the distribution divergence index to obtain the distribution similarity.

[0047] By using preset weighting coefficients to perform a weighted summation calculation on statistical feature similarity and distribution similarity, a global distribution similarity that represents the consistency of global statistical regularity of the sequence is obtained.

[0048] Optionally, the global morphological similarity, temporal warping similarity, feature matching score, and global distribution similarity are fused using multi-dimensional features to obtain a comprehensive evaluation score, including:

[0049] The initial values ​​of each perception weight coefficient are configured to be equal scores, and an index vector consisting of global morphological similarity, temporal warping similarity, feature matching score and global distribution similarity is constructed.

[0050] Calculate the mean of the elements of the index vector and obtain the dispersion of each similarity index relative to the mean of the elements;

[0051] Based on the discrete deviation, the visual saliency gain corresponding to each dimension is calculated using a preset nonlinear penalty function, and adaptive redistribution is performed on each perceptual weight coefficient through the visual saliency gain.

[0052] The global morphological similarity, temporal regularization similarity, feature matching score, and global distribution similarity are weighted and superimposed with the corresponding perceptual weight coefficients after dynamic redistribution to obtain a comprehensive evaluation score representing human eye perception.

[0053] The nonlinear penalty function is an exponential gain mapping function with discrete deviation as the independent variable. By performing nonlinear amplification on the negative discrete difference, the index dimension with the lower score obtains a higher visual significance gain, and the sum of the perceptual weight coefficients after weight allocation is a unit value.

[0054] Secondly, embodiments of the present invention provide a multidimensional temporal similarity evaluation system perceived by the human eye, comprising:

[0055] The data preprocessing module is used to obtain the real value sequence and predicted value sequence to be evaluated, and to perform benchmark alignment and fluctuation amplitude normalization processing to generate corresponding mapping sequence pairs under a unified observation field.

[0056] The global morphology analysis module is used to extract waveform geometric features of the mapping sequence pairs in local intervals using the sampling window, and obtain global morphological similarity based on the correlation strength of waveform geometric features in the spatial dimension.

[0057] The time warping evaluation module is used to establish nonlinear warping paths for mapping sequence pairs and perform exponential mapping on the cumulative cost generated by the path using the fluctuation scale of the mapping sequence pairs to obtain time warping similarity.

[0058] The feature anchor matching module is used to extract the local extreme points of each sequence in the mapping sequence pair as feature anchors, and obtain the feature matching score based on the offset distance of the mutually matching feature anchors in the time and amplitude dimensions of the mapping sequence pair.

[0059] The global distribution quantization module is used to extract the statistical moment features and statistical distribution evolution components of the mapped sequence pairs, and quantify the distribution consistency between the mapped sequence pairs in terms of statistical moment features and statistical distribution evolution components to obtain global distribution similarity.

[0060] The multidimensional perception fusion module is used to fuse global morphological similarity, temporal regularization similarity, feature matching score and global distribution similarity into a comprehensive evaluation score.

[0061] Thirdly, embodiments of the present invention provide a multi-dimensional time series similarity evaluation device for human eye perception, comprising: at least one controller; and a memory communicatively connected to the at least one controller; wherein the memory stores instructions executable by the at least one controller, the instructions being executed by the at least one controller to enable the at least one controller to perform the multi-dimensional time series similarity evaluation method for human eye perception as described above.

[0062] Fourthly, embodiments of the present invention provide a computer-readable storage medium storing computer-executable instructions, which, when executed by a controller, implement the multi-dimensional temporal similarity evaluation method perceived by the human eye as described above.

[0063] (III) Beneficial Effects

[0064] The beneficial effects of this invention are as follows: First, by performing benchmark alignment and fluctuation amplitude normalization on the true value sequence and the predicted value sequence, this invention constructs a mapping sequence pair under a unified observation field. Based on this, by extracting waveform geometric features using a sampling window and calculating their spatial correlation strength, global morphological similarity is obtained. This processing method solves the problems of traditional indicators (such as...) , Because it focuses on static numerical point-by-point comparison, it is difficult to capture the macroscopic evolution trend of the signal, which makes the evaluation process able to effectively identify the structured evolution of the waveform.

[0065] Furthermore, addressing the measurement noise and time delay effects commonly encountered in production, this invention utilizes nonlinear regularized paths to quantify the alignment quality of the time axis and combines this with exponential mapping processing based on fluctuation scales to effectively suppress the interference of slight temporal drift on the evaluation results. Simultaneously, by extracting local extrema as feature anchor points and quantifying the offset distance between mutually matching anchor points in both time and amplitude dimensions, this invention further obtains feature matching scores. This invention enhances the ability to capture key morphological features, achieves a unified evaluation of prediction accuracy and abnormal situations, and significantly improves the system's accuracy in capturing complex dynamic behaviors.

[0066] Furthermore, this invention quantifies the consistency of the probability density distribution of the mapped sequence by extracting statistical moment features and statistical distribution evolution components, thereby obtaining global distribution similarity. It supplements the density evolution features of numerical sequences, effectively distinguishing waveforms with similar values ​​but fundamentally different generation mechanisms or statistical patterns. Finally, based on preset human visual perception parameters, this invention fuses the similarity components of the above four dimensions using multi-dimensional features to ultimately obtain a comprehensive evaluation score.

[0067] Therefore, this invention reconstructs a multi-dimensional evaluation system for professionals observing time-series data from four dimensions: macroscopic profile, phase alignment, key events, and distribution density. This comprehensive evaluation system solves the technical problem of traditional indicators being severely mismatched with visual perception due to their single dimension, and can effectively eliminate evaluation bias caused by similar numerical values ​​but vastly different physical meanings. By outputting quantitative scores with high robustness, interpretability, and alignment with engineering intuition, this invention can not only accurately reflect the true matching status of complex chemical working conditions, but also provide a scientific basis that conforms to human visual perception logic for the defect diagnosis, performance evaluation, and automatic iteration of time-series prediction models. Attached Figure Description

[0068] Figure 1 This is a schematic diagram of the overall process of the method provided in the embodiments of the present invention;

[0069] Figure 2 This is a schematic diagram illustrating the specific process of step S1 of the method provided in this embodiment of the invention;

[0070] Figure 3 This is a detailed flowchart illustrating step S2 of the method provided in this embodiment of the invention;

[0071] Figure 4 This is a detailed flowchart illustrating step S3 of the method provided in this embodiment of the invention;

[0072] Figure 5 This is a detailed flowchart illustrating step S4 of the method provided in this embodiment of the invention;

[0073] Figure 6 This is a detailed flowchart illustrating step S5 of the method provided in this embodiment of the invention;

[0074] Figure 7 This is a detailed flowchart illustrating step S6 of the method provided in this embodiment of the invention;

[0075] Figure 8 This is a comparison chart of time series data for Sample 1 provided in an embodiment of the present invention;

[0076] Figure 9 This is a comparison chart of time series data for sample 2 provided in an embodiment of the present invention;

[0077] Figure 10 This is a comparison chart of time series data for sample 3 provided in an embodiment of the present invention;

[0078] Figure 11 This is a comparison chart of time series data for sample 4 provided in an embodiment of the present invention;

[0079] Figure 12 This is a comparison chart of time series data for sample 5 provided in an embodiment of the present invention;

[0080] Figure 13 This is a comparison chart of time series data for sample 6 provided in an embodiment of the present invention;

[0081] Figure 14 This is a comparison chart of time series data for sample 7 provided in an embodiment of the present invention;

[0082] Figure 15 This is a comparison chart of time series data for sample 8 provided in an embodiment of the present invention;

[0083] Figure 16 This is a comparison chart of time series data for sample 9 provided in an embodiment of the present invention. Detailed Implementation

[0084] To better explain and facilitate understanding of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0085] like Figure 1 As shown in the embodiment of the present invention, a method for evaluating multidimensional temporal similarity perceived by the human eye includes: acquiring the real value sequence and the predicted value sequence to be evaluated, and performing benchmark alignment and fluctuation amplitude normalization processing to generate corresponding mapping sequence pairs under a unified observation field; extracting waveform geometric features of the mapping sequence pairs in local intervals using a sampling window, and obtaining global morphological similarity based on the correlation strength of waveform geometric features in the spatial dimension; establishing a nonlinear regularized path for the mapping sequence pairs, and performing exponential mapping on the cumulative cost generated by the path using the fluctuation scale of the mapping sequence pairs to obtain time regularization similarity; extracting the local extreme points of each sequence in the mapping sequence pairs as feature anchors, and obtaining feature matching scores based on the offset distance of mutually matching feature anchors in the time and amplitude dimensions; extracting the statistical moment features and statistical distribution evolution components of the mapping sequence pairs, and quantifying the distribution consistency between the mapping sequence pairs in the statistical moment features and statistical distribution evolution components to obtain global distribution similarity; and fusing global morphological similarity, time regularization similarity, feature matching scores, and global distribution similarity in a multidimensional feature fusion to obtain a comprehensive evaluation score.

[0086] First, this invention constructs a mapping sequence pair under a unified observation field by performing benchmark alignment and fluctuation amplitude normalization on the true value sequence and the predicted value sequence. Based on this, global morphological similarity is obtained by extracting waveform geometric features using a sampling window and calculating their spatial correlation strength. This process solves the problems of traditional indicators (such as...) , Because it focuses on static numerical point-by-point comparison, it is difficult to capture the macroscopic evolution trend of the signal, which makes the evaluation process able to effectively identify the structured evolution of the waveform.

[0087] Furthermore, addressing the measurement noise and time delay effects commonly encountered in production, this invention utilizes nonlinear regularized paths to quantify the alignment quality of the time axis and combines this with exponential mapping processing based on fluctuation scales to effectively suppress the interference of slight temporal drift on the evaluation results. Simultaneously, by extracting local extrema as feature anchor points and quantifying the offset distance between mutually matching anchor points in both time and amplitude dimensions, this invention further obtains feature matching scores. This invention enhances the ability to capture key morphological features, achieves a unified evaluation of prediction accuracy and abnormal situations, and significantly improves the system's accuracy in capturing complex dynamic behaviors.

[0088] Furthermore, this invention quantifies the consistency of the probability density distribution of the mapped sequence by extracting statistical moment features and statistical distribution evolution components, thereby obtaining global distribution similarity. It supplements the density evolution features of numerical sequences, effectively distinguishing waveforms with similar values ​​but fundamentally different generation mechanisms or statistical patterns. Finally, based on preset human visual perception parameters, this invention fuses the similarity components of the above four dimensions using multi-dimensional features to ultimately obtain a comprehensive evaluation score.

[0089] Therefore, this invention does not perform numerical calculations in isolation, but reconstructs a multi-dimensional evaluation system for professionals observing time-series data from four dimensions: macroscopic profile, phase alignment, key events, and distribution density. This comprehensive evaluation system solves the technical problem of traditional indicators being severely mismatched with visual perception due to their single dimension, and can effectively eliminate evaluation bias caused by similar numerical values ​​but vastly different physical meanings. By outputting quantitative scores that are highly robust, interpretable, and aligned with engineering intuition, this invention can not only accurately reflect the true matching state of complex chemical engineering conditions, but also provide a scientific basis that conforms to human visual perception logic for the defect diagnosis, performance evaluation, and automatic iteration of time-series prediction models.

[0090] To better understand the above technical solutions, exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present invention are shown in the drawings, it should be understood that the present invention can be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that the present invention can be understood more clearly and thoroughly, and that the scope of the present invention can be fully conveyed to those skilled in the art.

[0091] Specifically, embodiments of the present invention provide a method for evaluating multidimensional temporal similarity perceived by the human eye, comprising:

[0092] S1. Obtain the true value sequence and predicted value sequence to be evaluated, and perform benchmark alignment and fluctuation amplitude normalization processing to generate corresponding mapping sequence pairs under a unified observation field.

[0093] Furthermore, such as Figure 2As shown, step S1 includes:

[0094] S11. Obtain a sequence of real values ​​consisting of at least one of the following: real-time data collected by industrial field physical sensors, historical observation records, or standard benchmark data; and a sequence of predicted values ​​generated by a preset time-series algorithm model. The preset time-series algorithm model includes, but is not limited to, an autoregressive moving average model. Exponential smoothing model, Long Short-Term Memory network Gated loop unit Temporal convolutional networks , The model or its derivative combination model.

[0095] S12. Calculate the first mean and first standard deviation corresponding to the true value sequence, and the second mean and second standard deviation corresponding to the predicted value sequence, respectively. In this embodiment, the true value sequence is calculated separately. mean with standard deviation and the predicted value sequence mean with standard deviation .

[0096] S13. A first centered sequence is obtained by subtracting the true value sequence from the first mean, and a second centered sequence is obtained by subtracting the predicted value sequence from the second mean. This aligns the waveform mean of each sequence to a zero-level reference, achieving reference alignment. Since different sensors may have calibration errors, or different batches of chemical production may have reference offsets, this process is performed... , The subtraction operation can effectively eliminate static offsets in the signal, so that the two curves are under the same zero-level reference, thereby avoiding misjudgment of similarity assessment caused by reference difference.

[0097] S14. Introduce a numerical stability constant to avoid division-by-zero anomalies. Summate the first standard deviation with the numerical stability constant to obtain a first fluctuation scaling factor, and sum the second standard deviation with the numerical stability constant to obtain a second fluctuation scaling factor. Wherein, the numerical stability constant... This is used to prevent calculation anomalies caused by a zero standard deviation in subsequent division operations. The standard deviation is added to the numerical stability constant to ensure that the denominator is never zero, thus mitigating the risk of overflow or program crashes when the computer performs subsequent division operations.

[0098] S15. The first centered sequence is divided using the first fluctuation scaling factor to obtain the mapped true value sequence, and the second centered sequence is divided using the second fluctuation scaling factor to obtain the mapped predicted value sequence. The mapped true value sequence and the mapped predicted value sequence constitute a mapped sequence pair under a unified observation field. This step achieves dimensionless processing through amplitude scaling. The specific calculation formula is as follows:

[0099] ;

[0100] Through the above mapping transformation, the final sequence of mapped true values ​​is obtained. With the mapping predicted value sequence All values ​​are constrained within a certain numerical distribution range. The resulting mapping sequence pairs provide a standardized and unified observation field for subsequent multi-dimensional similarity evaluation.

[0101] S2. Extract waveform geometric features of the mapping sequence pairs within the local interval using the sampling window, and obtain global morphological similarity based on the correlation strength of waveform geometric features in the spatial dimension.

[0102] Furthermore, such as Figure 3 As shown, step S2 includes:

[0103] S21. Based on the maximum and minimum values ​​of the mapped true value sequence and the numerical stability constant, the dynamic range is determined. A proportional mapping is performed on the dynamic range using preset coefficients, and the mapping result is subjected to power transformation and numerical bias processing to obtain the first smoothing factor and the second smoothing factor. Before performing local similarity calculations, global parameters are first determined to ensure the adaptability of the evaluation. First, the mapped true value sequence is calculated. dynamic range The calculation formula is: Then, based on the preset coefficients and The first smoothing factor is calculated. With the second smoothing factor The specific formula is as follows: , Here, power transformation (square operation) and numerical bias (superposition) are used. This process ensures that the denominator is not zero when the sequence fluctuation is extremely small, thus enhancing the numerical stability of the algorithm.

[0104] S22. A sliding traversal is performed along the time axis of the mapped sequence pairs using a preset sampling window to extract the corresponding local sequences of the mapped true values ​​and the local sequences of the mapped predicted values ​​at each sampling position. In this step, the sampling window size is set to... (In this embodiment, the value is typically taken as) , for (Sequence length). Utilizing a window with a total length of... The timeline is slidable, and the sliding range is... to At each sliding position By extracting segments of corresponding lengths, a local sequence of mapped real values ​​can be obtained. Local sequence of mapped predicted values This process simulates the scanning mechanism by which the human eye captures local morphological details by shifting the visual focus when observing long sequences.

[0105] S23. Calculate the waveform geometric features corresponding to each sampling position. The waveform geometric features include the local mean and local standard deviation of the local sequence of mapped true values ​​and the local sequence of mapped predicted values, as well as the local covariance between the local sequence of mapped true values ​​and the local sequence of mapped predicted values. For the first... For local sequences within a window, the waveform geometric features reflecting their geometric distribution characteristics are calculated, as follows:

[0106] Local mean: , ;

[0107] Local standard deviation:

[0108] ;

[0109] Local covariance: ;

[0110] Here, the mean represents the local brightness (baseline level) of the waveform, the standard deviation represents the local contrast (fluctuation intensity), and the covariance quantifies the degree of structural correlation between the two sets of sequences in terms of spatial morphology.

[0111] S24. Using the first and second smoothing factors, perform product summation and ratio calculations on the local mean, local standard deviation, and local covariance to obtain the local structural similarity index corresponding to the current sampling position. Substitute the obtained smoothing factors and waveform geometric features into the structural similarity calculation model to calculate the... SSIM (Short Component Similarity Index) for local structures of a window k :

[0112] ;

[0113] This formula comprehensively evaluates the fusion similarity of two local waveforms in terms of brightness consistency, contrast consistency, and structural correlation by comparing the product terms of the numerator and denominator. The closer the score is to 1, the more consistent the local geometric shape is.

[0114] S25. Perform an arithmetic mean on all local structural similarity indices generated during the sliding traversal to obtain the global morphological similarity, which characterizes the overall contour consistency of the waveform. After completing the sliding traversal of the entire sequence, collect the local index sequences generated at all sampling positions. Global morphological similarity is calculated using the arithmetic mean method. :

[0115] ;

[0116] In the formula, the obtained As a core component for quantizing the similarity of the mapping sequence to the global contour, it effectively solves the technical problem that traditional global indicators fail due to severe local fluctuations in time series.

[0117] S3. Establish a nonlinear regularized path for the mapping sequence pair, and perform exponential mapping on the cumulative cost generated by the path using the fluctuation scale of the mapping sequence pair to obtain the time regularized similarity.

[0118] Furthermore, such as Figure 4 As shown, step S3 includes:

[0119] S31. Calculate the absolute numerical difference between the true value sequence and the predicted value sequence of the mapping point by point, and construct a local distance matrix to store the point-to-point metric cost.

[0120] In this embodiment, the lengths are first traversed using a double loop. and Mapping of the true value sequence With the mapping predicted value sequence (in = For each pair of time points. Calculate the absolute difference in their values. This allows us to construct a local distance matrix, which is used to quantify the original deviation between any two points in the magnitude dimension.

[0121] S32. Construct a cumulative distance matrix to store path accumulation values ​​based on the length of the mapping sequence pairs, and perform initialization processing on the cumulative distance matrix, including zeroing the starting position and defining the boundary maxima, to establish boundary guiding constraints for the nonlinear regular path search. Construct a matrix with dimension... Cumulative distance matrix To ensure that the path is forcibly started from the beginning of the sequence, the following initialization operation is performed: Set the initial alignment cost... At the same time, the boundary elements are defined as maxima, i.e. as well as This initialization process establishes a physical barrier to the search space, guiding the optimization algorithm to start from the coordinates. Start towards Evolution.

[0122] S33. Within the boundary guidance constraints and the search range determined by the preset window radius, based on the local distance matrix and through cost recursion optimization logic, the cumulative distance matrix is ​​cumulatively superimposed to generate the minimum cumulative cost matrix recording the sequence from its starting position to each corresponding position. The minimum cumulative cost matrix is ​​then used to establish a nonlinear regularized path between mapping sequence pairs. To prevent distortion of physical meaning caused by path warping, this embodiment introduces a preset window radius. During the recursive process, for each row... It performs calculations only within the specified search window, and its search interval is... ,in Within this range, the matrix is ​​updated using the following cost recursive formula. :

[0123] ;

[0124] This recursive logic simulates the visual mechanism by which the human eye automatically searches for alignment points of peaks or troughs within a small range when comparing two curves with phase discrepancies, thereby establishing an optimal matching path across the time axis offset in the cumulative distance matrix.

[0125] S34. Extract the value corresponding to the last position of the minimum cumulative cost matrix as the total cumulative cost generated by the nonlinear normalization path. After completing the iterative calculation of the entire matrix, extract the last cell of the minimum cumulative cost matrix. The value at that point represents the minimum overall cost, or total cumulative distance, required for two sequences to achieve time axis alignment under the optimal nonlinear regularization path.

[0126] S35. Determine the fluctuation scaling factor based on the length, standard deviation, and numerical stability constant of the mapped true value sequence, and perform a ratio operation between the total cumulative cost and the fluctuation scaling factor to obtain the normalized path weight. To ensure the comparability of chemical signals with different lengths and fluctuation characteristics, this embodiment constructs a fluctuation scaling factor. The calculation formula is as follows: ,in The standard deviation of the obtained mapped true value sequence is used. Then, the ratio of the total cumulative cost to the volatility scaling factor is calculated to obtain the normalized path weights. .

[0127] S36. Using exponential mapping, the negative values ​​of the normalized path weights are transformed into time-warped similarity, representing the degree of temporal alignment between sequences. Finally, the cost component is transformed into a similarity component through the exponential mapping function, and the time-warped similarity is calculated. :

[0128] ;

[0129] This mapping process ensures that when two sequences are perfectly aligned ( When =0), The value is 1; however, the larger the phase deviation or numerical difference, the better. The closer it is to 0, the better. This approach gives the algorithm excellent robustness to slight temporal drift and enables it to accurately reflect the degree of consistency between chemical operating conditions and the time axis.

[0130] S4. Extract the local extreme points of each sequence in the mapping sequence pair as feature anchors, and obtain the feature matching score based on the offset distance of the mutually matching feature anchors in the time and amplitude dimensions.

[0131] Furthermore, such as Figure 5 As shown, step S4 includes:

[0132] S41. Perform local extremum retrieval on the mapping true value sequence and the mapping predicted value sequence according to the significance threshold determined by the standard deviation of the mapping true value sequence. Sort the retrieved local maxima points in descending order according to the magnitude significance and retain a preset number of feature anchor points to obtain the mapping true value feature anchor point set and the mapping predicted value feature anchor point set.

[0133] When performing feature extraction, the first step is to use the standard deviation of the mapped true value sequence. Calculate the significance threshold ,in This threshold is used to ensure basic retrieval sensitivity in extremely stationary sequences. It is then used to map the true value sequence. With the mapping predicted value sequence Perform local extremum retrieval separately (e.g., using...) ), to obtain the initial peak point set and Then, they are sorted in descending order based on the amplitude of each peak point, and the top-ranked peaks are retained. The most significant peak points are used as feature anchor points to construct a feature anchor point set that maps to the true values. With the feature anchor set of the mapped predicted value ,in This is an amplitude descending sort operator, used to arrange the extracted peaks from largest to smallest in absolute height. This process simulates the feature extraction mechanism of human vision, which automatically ignores minute glitch information and focuses on significant abrupt changes or key inflection points in the waveform.

[0134] S42. For each true value feature anchor point in the set of mapped true value feature anchor points, use the nearest neighbor search algorithm to match the corresponding associated anchor point in the set of mapped predicted value feature anchor points, and calculate the time offset between the true value feature anchor point and the matched mapped predicted value feature anchor point. For The location of each feature anchor point in In the predicted value anchor set Perform a nearest neighbor search to find the associated anchor point that is closest to it on the timeline. The search logic is as follows: After identifying the matching pair, calculate the absolute time offset between them. and the corresponding amplitude deviation .

[0135] S43. Determine if the time offset exceeds the maximum lag determined by the length of the mapped true value sequence. To ensure the physical plausibility of the match, a maximum allowable lag window is set. This is based on the length of the mapped true value sequence. Calculate the maximum lag. ,in The maximum permissible time lag is defined as the extreme upper limit of the time axis offset of the predicted peak relative to the true peak during peak matching. This is the time delay coefficient, which is usually set according to the delay characteristics of the industrial process (e.g., 0.05).

[0136] S44. If the time offset exceeds the maximum hysteresis, then the local matching component corresponding to the current true value feature anchor point is set to zero. When detected... If the event fails to effectively capture the preset specific characteristic event, or if the captured event has lost its engineering reference significance in the time dimension, then the true value feature anchor point is removed. Corresponding local matching components It will be recorded as 0 points.

[0137] S45. If the time offset does not exceed the maximum lag, calculate the positional offset distance and amplitude deviation distance between the ground truth feature anchor point and the matched mapped predicted feature anchor point. Then, using the positional decay scale and amplitude decay scale determined based on the length and standard deviation of the mapped ground truth sequence, perform exponential decay mapping on the positional offset distance and amplitude deviation distance to obtain the corresponding local matching components. When the time offset is within the allowable range, a Gaussian kernel function is used to smoothly model the offset distance. First, determine the positional decay scale. and amplitude attenuation scale Using the above scale parameters, the time migration is... With amplitude offset Perform joint exponential decay mapping and compute local matching components. :

[0138] ;

[0139] This formula ensures that the local matching component is close to 1 only when the predicted feature point closely matches the real feature point in both the time and amplitude dimensions, thus achieving a refined quantification of the accuracy of predictions for key physical events.

[0140] S46. Perform an arithmetic mean on all the local matching components determined by each true value feature anchor point to obtain the feature matching score that represents the degree of alignment of the mapping sequence pair at the morphological features.

[0141] After traversing After identifying all feature anchor points, the mean of the obtained local matching components is calculated, and the final feature matching score is then determined.

[0142] ;

[0143] The score It is specifically designed to measure the predictive performance of extreme conditions or transient changes in industrial production processes.

[0144] S5. Extract the statistical moment features and statistical distribution evolution components of the mapped sequence pairs, and quantify the distribution consistency between the mapped sequence pairs in terms of statistical moment features and statistical distribution evolution components to obtain the global distribution similarity.

[0145] Furthermore, such as Figure 6 As shown, step S5 includes:

[0146] S51. Extract multi-order statistical moment features, including mean, standard deviation, skewness, and kurtosis, from both the mapped true value sequence and the mapped predicted value sequence, and construct corresponding statistical moment feature vectors using these features. First, starting from the structural characteristics of the numerical distribution, extract statistical features in four dimensions. For the mapped true value sequence... With the mapping predicted value sequence Calculate separately:

[0147] Mean: , ;

[0148] Standard deviation: , ;

[0149] Skewness, used to quantify the degree of asymmetry in a distribution:

[0150] , ;

[0151] Kurtosis, used to quantify the sharpness or smoothness of a distribution:

[0152] , ;

[0153] Among them, expectation operation Characterizes the arithmetic or statistical average processing performed on sample points within each sequence, used to quantify the central moments of the corresponding sequence in the sample space.

[0154] Finally, the statistical moment eigenvectors are constructed:

[0155] , .

[0156] S52. Calculate the relative difference between the statistical moment eigenvectors of the mapped true value sequence and the mapped predicted value sequence, and perform a nonlinear transformation on the mean of the relative difference using a negative exponential mapping to obtain the statistical feature similarity. To eliminate the differences in numerical magnitude between different orders of statistical moments, calculate the similarity of each feature dimension. Relative degree of difference:

[0157] ;

[0158] Subsequently, statistical feature similarity is calculated by performing a negative exponential transformation on the mean of the relative differences across the four dimensions. :

[0159] ;

[0160] This indicator reflects the degree of macroscopic agreement between the two sets of data in terms of basic statistical patterns.

[0161] S53. Calculate the numerical histograms of the mapped true value sequence and the mapped predicted value sequence according to the preset number of bins, and perform normalization processing to obtain the statistical distribution evolution components characterizing the numerical density features of the sequence. To obtain finer-grained numerical density features within the sequence, the value range is equally divided into... For each interval, the frequency of occurrence in each interval is counted to obtain the original histogram. and Next, a numerical stability constant is added, and full probability normalization is performed:

[0162] , ;

[0163] The normalized histogram is the statistical distribution evolution component, which represents the probability distribution of the signal's evolution in different amplitude ranges.

[0164] S54. Calculate the distribution divergence index between the statistical distribution evolution components of the mapped true value sequence and the mapped predicted value sequence, and perform exponential mapping processing based on a preset scaling factor on the distribution divergence index to obtain the distribution similarity. This step introduces... divergence ( This is used to quantify the difference between the two distribution components. First, the intermediate distribution is calculated. Then use divergence calculate :

[0165] ;

[0166] Subsequently, an exponential transformation is performed using a preset scaling factor (set to 3 in this embodiment) to obtain the distribution similarity. : . The introduction of [the technology] solved the traditional [problem]. The problem of divergence asymmetry allows the distribution similarity to more stably reflect the consistency of the two sets of chemical parameters in terms of generation mechanism.

[0167] S55. Using preset weighting coefficients, perform a weighted summation calculation on the statistical feature similarity and distribution similarity to obtain the global distribution similarity, which represents the consistency of the global statistical regularity of the sequence. Finally, calculate the global distribution similarity by linearly weighting and fusing the two statistical sub-components: This proportional allocation (0.6 and 0.4) balances the stability of the basic statistical moments with the sensitivity of the numerical distribution pattern, thereby achieving a comprehensive characterization of the global statistical characteristics of long-term data.

[0168] S6. Multi-dimensional feature fusion is performed on global morphological similarity, temporal regularization similarity, feature matching score and global distribution similarity to obtain a comprehensive evaluation score.

[0169] Furthermore, such as Figure 7 As shown, step S6 includes:

[0170] S61. Configure the initial value of each perception weight coefficient as an equal score, and construct an index vector consisting of global morphological similarity, time-warped similarity, feature matching score and global distribution similarity.

[0171] First, the global morphological similarity is... Time regularization similarity Feature matching score and global distribution similarity Perceptual weight coefficients in four dimensions Initialize the scores to equal values, meaning each dimension's initial weight is set to 0.25. Then, use these four indicators as elements to construct a four-dimensional indicator vector. .

[0172] S62. Calculate the mean of the elements in the index vector and obtain the dispersion deviation of each similarity index relative to the mean of the elements. Calculate the index vector. internal element mean Then, the difference between the similarity index of each dimension and the mean is calculated in turn to obtain the dispersion deviation of each dimension. This deviation reflects the severity of numerical conflict between different evaluation dimensions; when a certain dimension (such as feature matching) When the deviation is significantly lower than the average level, the dispersion is positive and large, indicating that the model has serious defects in this specific domain.

[0173] S63. Based on the discrete deviation, calculate the visual saliency gain corresponding to each dimension using a preset nonlinear penalty function, and perform adaptive redistribution of each perceptual weight coefficient through the visual saliency gain; wherein, the nonlinear penalty function is an exponential gain mapping function with discrete deviation as the independent variable, and performs nonlinear amplification processing on the negative discrete difference so that the index dimension with the lower score obtains a higher visual saliency gain, and the sum of each perceptual weight coefficient after weight redistribution is a unit value.

[0174] In this step, the discrete deviation is used. Given an exponential gain mapping function for the independent variable, calculate the visual saliency gain for each dimension. :

[0175] ;

[0176] In the formula, Represents a dimension index. This is a preset sensitivity adjustment coefficient (e.g., a value between 1 and 5). The function adjusts the positive difference, which characterizes the degree of negative deviation. Nonlinear amplification is performed to give higher weights to the visual saliency gain of the indicator dimensions with lower scores.

[0177] Subsequently, an adaptive redistribution is performed on each initial weight based on this gain to obtain the final perceptual weight coefficients. :

[0178] ;

[0179] In the formula, For the first The initial values ​​of the perceptual weight coefficients for each dimension. For cumulative indexing, All values ​​are taken from the set {1, 2, 3, 4}. This mechanism ensures that the sum of the perceived weight coefficients after weight allocation is always a unit value of 1.

[0180] It is important to emphasize that, under typical operating conditions in this embodiment, the aforementioned adaptive adjustment logic aims to ensure that the final generated weight allocation converges in real time to the visual intuition of engineering experts, taking into account any shortcomings in the indicators. For example, when the indicators are balanced, the recommended baseline distribution tends to be: , , , This weighting reflects that when comparing two chemical curves, the human eye first focuses on the overall contour evolution (morphology has the highest weight), and then on the timing alignment quality and key process events (such as peak alignment).

[0181] S64. The global morphological similarity, temporal regularization similarity, feature matching score and global distribution similarity are weighted and superimposed with the corresponding perceptual weight coefficients after dynamic redistribution to obtain a comprehensive evaluation score representing human eye perception.

[0182] Finally, the scores from the four dimensions generated in steps S2 to S5 are linearly weighted and fused with the determined weight coefficients to calculate the comprehensive evaluation score: The overall rating The value range is strictly limited to the interval [0,1]. The closer the score is to 1, the higher the correlation between the predicted curve and the actual curve across multiple dimensions of human perception, providing highly interpretable decision support for evaluating prediction accuracy, analyzing the reliability of anomaly warnings, and assessing model performance in chemical production processes. Furthermore, since this score consists of four independent components, the output... At the same time, it can also display the scores of each dimension, thereby helping technicians to accurately locate the model's shortcomings in specific dimensions (such as phase shift or peak prediction ability).

[0183] In one specific embodiment, for verification The feasibility and discriminative power of multi-dimensional similarity evaluation indicators under different similarity levels were tested using nine different experimental samples. The experimental results can be divided into three evaluation gradients: high, medium, and low, based on the degree of sequence matching. The specific analysis is as follows.

[0184] First, in highly similar scenarios, such as Figures 8 to 10 As shown, the curves comparing the predicted and actual values ​​of the three time series data points correspond to... The scores were 0.934, 0.921, and 0.910, respectively. This quantitative evaluation result is consistent with the visual performance, which closely matches the curves shown in the figure, validating the... The indicator is consistent with human visual perception in assessing highly similar sequences.

[0185] Secondly, in scenarios with moderate similarity, Figures 11 to 13The evaluation results further demonstrate The distinguishing power of the indicators was scored at 0.580, 0.875, and 0.683, respectively, reflecting significant differences in the level of similarity between different sequences. Specifically, Figure 12 It exhibits high prediction accuracy, while Figure 11 and Figure 13 There are identifiable local biases. This result indicates that... The indicator can not only identify high-quality predictions, but also effectively quantify situations with low to medium similarity, demonstrating its sensitivity in a wide range of assessments.

[0186] Subsequently, in scenarios where the model fails or deviates significantly from the intended scenario, such as Figures 14 to 16 In the case, The scores of 0.198, 0.293, and 0.173 indicate a significant difference between the predicted and actual sequences. This metric effectively captures the failure of the prediction model in this scenario, consistent with the deviation visually shown in the figure, proving its effectiveness. It has a reliable ability to judge from highly consistent to significantly different in the complete similarity assessment spectrum.

[0187] Furthermore, this invention provides three implementation schemes for different industrial application needs:

[0188] In a first embodiment, the present invention provides a simplified three-dimensional evaluation combination. This scheme mainly consists of global morphological similarity. Time regularization similarity and feature matching score The core logic of this solution lies in eliminating computational steps sensitive to global statistical characteristics and instead focusing on the local morphology and time alignment quality of the waveform. This approach is particularly suitable for industrial scenarios that are insensitive to overall statistical distribution but have extremely high requirements for local morphological evolution and time alignment accuracy during the production process. The corresponding fusion formula is:

[0189] .

[0190] in, These are the preset weights after normalization.

[0191] In a second implementation, the present invention provides an extended five-dimensional evaluation combination. This scheme, based on the original four-dimensional features (morphology, time, feature points, and statistical distribution), further introduces trend similarity. and the corresponding weights In practice, linear regression analysis is performed on the sequence to calculate and compare the regression slopes of the mapped true value sequence and the mapped predicted value sequence, thereby quantifying their consistency in trend direction. This scheme can more accurately characterize the long-range evolution trend of the signal, and its corresponding fusion formula is:

[0192] .

[0193] This multi-dimensional and in-depth integration provides a more rigorous quantitative method for industrial time series with strong trend characteristics.

[0194] In a third embodiment, the present invention provides a similarity evaluation method based on frequency domain features. For industrial signals with significant periodicity, this method transforms the mapped sequence pairs into the frequency domain space and obtains frequency domain similarity by comparing the similarity of the main frequency components. The specific calculation process includes: obtaining the frequency domain components of the true value using Fourier transform. Frequency domain components of the predicted value Subsequently, the frequency domain similarity is calculated using the following formula:

[0195] ;

[0196] in, The index represents the frequency component. A significant advantage of this scheme is its insensitivity to time axis shifts or local offsets, allowing it to more objectively reflect the predictive model's ability to capture periodic waveform features, making it particularly suitable for monitoring scenarios with periodic requirements.

[0197] Furthermore, embodiments of the present invention provide a multidimensional temporal similarity evaluation system perceived by the human eye, comprising: a data preprocessing module, used to acquire the real value sequence and predicted value sequence to be evaluated, and perform benchmark alignment and fluctuation amplitude normalization processing to generate corresponding mapping sequence pairs under a unified observation field; a global morphological analysis module, used to extract waveform geometric features of the mapping sequence pairs in local intervals using a sampling window, and obtain global morphological similarity based on the correlation strength of waveform geometric features in the spatial dimension; and a time warping evaluation module, used to establish a nonlinear warping path for the mapping sequence pairs, and perform exponential mapping on the cumulative cost generated by the path using the fluctuation scale of the mapping sequence pairs. The system employs several methods to obtain a comprehensive evaluation score. The first method extracts time-warped similarity. The second method uses a feature anchor matching module to extract local extrema of each sequence in the mapped sequence pair as feature anchors. Based on the offset distance of the matched feature anchors in the time and amplitude dimensions, it obtains a feature matching score. The third method extracts statistical moment features and statistical distribution evolution components of the mapped sequence pair and quantifies the distribution consistency between the mapped sequence pairs in these features, obtaining a global distribution similarity. The fourth method integrates global morphological similarity, time-warped similarity, feature matching score, and global distribution similarity to obtain a comprehensive evaluation score.

[0198] Meanwhile, embodiments of the present invention provide a multi-dimensional time series similarity evaluation device for human visual perception, comprising: at least one controller; and a memory communicatively connected to the at least one controller; wherein the memory stores instructions executable by the at least one controller, the instructions being executed by the at least one controller to enable the at least one controller to perform the multi-dimensional time series similarity evaluation method for human visual perception as described above.

[0199] Furthermore, embodiments of the present invention provide a computer-readable storage medium storing computer-executable instructions, which, when executed by a controller, implement the multidimensional temporal similarity evaluation method perceived by the human eye as described above.

[0200] In summary, the embodiments of the present invention provide a method, system, device, and medium for evaluating multidimensional temporal similarity perceived by the human eye. This scheme obtains the real value sequence and the predicted value sequence to be evaluated and performs benchmark alignment and normalization preprocessing. Then, it comprehensively extracts the similarity components of the mapping sequence pairs in multiple dimensions such as waveform geometric features, nonlinear regularization paths, feature anchor point offsets, and statistical distribution evolution components. Based on preset human visual perception parameters, it performs multidimensional feature fusion, thereby constructing a dedicated evaluation system for prediction and anomaly detection.

[0201] This scheme utilizes multi-dimensional similarity metrics to quantify the degree of agreement between actual and predicted values ​​in time series forecasting, achieving a unified assessment of prediction accuracy and anomalies. Through dimensional design tailored to the prediction task, this invention specifically defines phase similarity to evaluate time alignment quality and key point matching degree to measure the accuracy of key events in both temporal and amplitude dimensions, thus accurately reflecting the prediction model's ability to capture dynamic behavior. Simultaneously, this invention possesses excellent diagnostic capabilities and interpretability. By outputting independent scores for each dimension, it can clearly indicate specific shortcomings of the prediction model in areas such as morphological fitting, temporal alignment, key event capture, or overall distribution consistency, providing clear optimization directions for the model's iterative evolution.

[0202] Furthermore, because this solution constructs a feature space based on multi-dimensional score vectors, it can achieve fine-grained classification oriented towards anomaly types, automatically identifying different anomaly patterns such as morphological anomalies, phase shifts, or peak absence. By integrating the above-mentioned methods into hardware and software systems or dedicated devices, this invention can automate the testing, evaluation, and diagnosis of time series prediction models in real-world industrial environments, ensuring that the evaluation results are highly consistent with the intuition of domain experts. This effectively overcomes the problem of traditional indicators such as mean squared error or mean absolute error being disconnected from expert subjective judgment, making the evaluation results more aligned with engineering practice and easier for professionals to understand and adopt.

[0203] Furthermore, this invention, through a comprehensive design incorporating structural similarity and phase alignment, effectively suppresses the impact of common noise interference and slight temporal drift in industrial data, significantly improving the stability and reliability of the evaluation process. This evaluation framework, possessing model diagnostic and insight capabilities, not only accurately locates model defects but also demonstrates broad adaptability to various scenarios. It is not only applicable to regression prediction tasks but can also be extended to various time-series analysis scenarios such as anomaly detection and generative model evaluation, providing a unified and scientific evaluation standard for different application needs.

[0204] Since the systems / devices described in the above embodiments of the present invention are systems / devices used to implement the methods of the above embodiments of the present invention, those skilled in the art can understand the specific structure and modifications of the systems / devices based on the methods described in the above embodiments of the present invention, and therefore will not be repeated here. All systems / devices used in the methods of the above embodiments of the present invention fall within the scope of protection of the present invention.

[0205] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0206] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions.

[0207] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the claims should be interpreted to include both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0208] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, then this invention should also include these modifications and variations.

Claims

1. A method for evaluating multidimensional temporal similarity perceived by the human eye, characterized in that, include: Obtain the true value sequence and predicted value sequence to be evaluated, and perform benchmark alignment and fluctuation amplitude normalization to generate corresponding mapping sequence pairs under a unified observation field; The sampling window is used to extract the waveform geometric features of the mapping sequence pairs in the local interval, and the global morphological similarity is obtained based on the correlation strength of the waveform geometric features in the spatial dimension. Nonlinear warping paths are established for mapping sequence pairs, and exponential mapping is performed on the cumulative cost generated by the path using the fluctuation scale of the mapping sequence pairs to obtain time warping similarity. Local extreme points of each sequence in the mapping sequence pair are extracted as feature anchors, and feature matching scores are obtained based on the offset distance of the mutually matching feature anchors in the time and amplitude dimensions of the mapping sequence pair. Extract the statistical moment features and statistical distribution evolution components of the mapped sequence pairs, and quantify the distribution consistency of the mapped sequence pairs in terms of statistical moment features and statistical distribution evolution components to obtain the global distribution similarity; The global morphological similarity, temporal regularity similarity, feature matching score, and global distribution similarity are fused into a multi-dimensional feature to obtain a comprehensive evaluation score.

2. The multidimensional temporal similarity evaluation method for human visual perception as described in claim 1, characterized in that, Obtain the true value sequence and predicted value sequence to be evaluated, and perform benchmark alignment and fluctuation amplitude normalization processing to generate corresponding mapping sequence pairs under a unified observation field, including: Acquire a sequence of real values ​​consisting of at least one of the following: real-time data collected by physical sensors at the industrial site, historical observation records, or standard benchmark data; and a sequence of predicted values ​​generated by a preset time-series algorithm model. Calculate the first mean and first standard deviation corresponding to the true value sequence, and the second mean and second standard deviation corresponding to the predicted value sequence, respectively; The first centered sequence is obtained by subtracting the true value sequence using the first mean, and the second centered sequence is obtained by subtracting the predicted value sequence using the second mean, so as to align the waveform mean of each sequence to the zero-level reference and achieve reference alignment. A numerical stability constant is introduced to avoid the division-to-zero anomaly. The first fluctuation scaling factor is obtained by summing the first standard deviation with the numerical stability constant, and the second fluctuation scaling factor is obtained by summing the second standard deviation with the numerical stability constant. The first centering sequence is divided using the first fluctuation scaling factor to obtain the mapped true value sequence, and the second centering sequence is divided using the second fluctuation scaling factor to obtain the mapped predicted value sequence. The mapped true value sequence and the mapped predicted value sequence constitute a mapped sequence pair under a unified observation field.

3. The multidimensional temporal similarity evaluation method for human visual perception as described in claim 2, characterized in that, The sampling window is used to extract waveform geometric features of the mapped sequence pairs within local intervals, and global morphological similarity is obtained based on the correlation strength of waveform geometric features in the spatial dimension, including: The dynamic range is determined based on the maximum and minimum values ​​of the mapped true value sequence and the numerical stability constant. The dynamic range is proportionally mapped using preset coefficients, and the mapping result is subjected to power transformation and numerical bias processing to obtain the first smoothing factor and the second smoothing factor. A sliding traversal is performed along the time axis of the mapping sequence pairs using a preset sampling window to extract the corresponding local sequence of the true mapping value and the local sequence of the predicted mapping value at each sampling position. Calculate the waveform geometric features corresponding to each sampling position. The waveform geometric features include the local mean and local standard deviation of the local sequence of the mapped true value and the local sequence of the mapped predicted value, as well as the local covariance between the local sequence of the mapped true value and the local sequence of the mapped predicted value. Using the first and second smoothing factors, the local mean, local standard deviation and local covariance are multiplied and ratioed to obtain the local structural similarity index corresponding to the current sampling position. The arithmetic mean of all local structural similarity indices generated during the sliding traversal is performed to obtain the global morphological similarity that characterizes the overall contour consistency of the waveform.

4. The multidimensional temporal similarity evaluation method for human visual perception as described in claim 2, characterized in that, Nonlinear warped paths are established for mapped sequence pairs, and exponential mapping is performed on the cumulative cost generated by the path using the fluctuation scale of the mapped sequence pairs to obtain time-warped similarity, including: The absolute numerical difference between the mapped true value sequence and the mapped predicted value sequence is calculated point by point, and a local distance matrix is ​​constructed to store the point-to-point metric cost. Based on the length of the mapping sequence pairs, a cumulative distance matrix is ​​constructed to store the cumulative values ​​of the paths. An initialization process, including zeroing the starting position and defining the boundary maxima, is performed on the cumulative distance matrix to establish the boundary guiding constraints for the nonlinear regular path search. Within the boundary guidance constraints and the search range determined by the preset window radius, the cumulative distance matrix is ​​cumulatively superimposed based on the local distance matrix and the cost recursive optimization logic to generate the minimum cumulative cost matrix from the start position of the sequence to each corresponding position, and the minimum cumulative cost matrix is ​​used to establish a nonlinear regularized path between the mapping sequence pairs. Extract the value corresponding to the end position of the minimum cumulative cost matrix as the total cumulative cost generated by the nonlinear regularization path; The fluctuation scale factor is determined based on the length, standard deviation and numerical stability constant of the mapped true value sequence, and the normalized path weight is obtained by performing a ratio operation between the total cumulative cost and the fluctuation scale factor. Exponential mapping is used to transform the negative values ​​of normalized path weights into time regularization similarity, which represents the degree of time axis alignment between sequences.

5. The multidimensional temporal similarity evaluation method for human visual perception as described in claim 2, characterized in that, Local extrema of each sequence in the mapped sequence pair are extracted as feature anchors. Based on the offset distances of the matching feature anchors in the time and magnitude dimensions of the mapped sequence pair, feature matching scores are obtained, including: Local extremum retrieval is performed on the mapping true value sequence and the mapping predicted value sequence according to the significance threshold determined by the standard deviation of the mapping true value sequence. The retrieved local maxima points are sorted in descending order according to the magnitude significance and a preset number of feature anchor points are retained to obtain the mapping true value feature anchor point set and the mapping predicted value feature anchor point set. For each true value feature anchor in the set of true value feature anchors, the nearest neighbor search algorithm is used to match the corresponding associated anchor in the set of predicted value feature anchors, and the time offset between the true value feature anchor and the matched predicted value feature anchor is calculated. Determine whether the time offset exceeds the maximum lag determined by the length of the mapped true value sequence; If the time offset exceeds the maximum lag, the local matching component corresponding to the current true value feature anchor point will be set to zero. If the time offset does not exceed the maximum lag, the position offset distance and amplitude deviation distance between the true value feature anchor point and the matched mapped predicted value feature anchor point are calculated. Then, using the position decay scale and amplitude decay scale determined based on the length and standard deviation of the mapped true value sequence, exponential decay mapping is performed on the position offset distance and amplitude deviation distance to obtain the corresponding local matching component. For each true value feature anchor point, perform an arithmetic mean on all the local matching components to obtain the feature matching score that represents the degree of alignment of the mapping sequence pair at the morphological features.

6. The method for evaluating multidimensional temporal similarity perceived by the human eye as described in claim 1, characterized in that, Extract the statistical moment features and statistical distribution evolution components of the mapped sequence pairs, and quantify the distributional consistency between the mapped sequence pairs in terms of statistical moment features and statistical distribution evolution components to obtain global distributional similarity, including: For the mapped true value sequence and the mapped predicted value sequence, multi-order statistical moment features including mean, standard deviation, skewness and kurtosis are extracted respectively, and corresponding statistical moment feature vectors are constructed using the multi-order statistical moment features respectively; The relative difference between each feature component of the statistical moment eigenvectors of the mapped true value sequence and the mapped predicted value sequence is calculated, and the mean of the relative difference is nonlinearly transformed using negative exponential mapping to obtain the statistical feature similarity. According to the preset number of bins, the numerical histograms of the mapped true value sequence and the mapped predicted value sequence are statistically analyzed, and normalization is performed to obtain the statistical distribution evolution components that characterize the numerical density features of the sequence. Calculate the distribution divergence index between the statistical distribution evolution components of the mapped true value sequence and the mapped predicted value sequence, and perform exponential mapping processing based on a preset scaling factor on the distribution divergence index to obtain the distribution similarity. By using preset weighting coefficients to perform a weighted summation calculation on statistical feature similarity and distribution similarity, a global distribution similarity that represents the consistency of global statistical regularity of the sequence is obtained.

7. The method for evaluating multidimensional temporal similarity perceived by the human eye as described in any one of claims 1-6, characterized in that, A multi-dimensional feature fusion method is used to obtain a comprehensive evaluation score, which includes: global morphological similarity, temporal warping similarity, feature matching score, and global distribution similarity. The initial values ​​of each perception weight coefficient are configured to be equal scores, and an index vector consisting of global morphological similarity, temporal warping similarity, feature matching score and global distribution similarity is constructed. Calculate the mean of the elements of the index vector and obtain the dispersion of each similarity index relative to the mean of the elements; Based on the discrete deviation, the visual saliency gain corresponding to each dimension is calculated using a preset nonlinear penalty function, and adaptive redistribution is performed on each perceptual weight coefficient through the visual saliency gain. The global morphological similarity, temporal regularization similarity, feature matching score, and global distribution similarity are weighted and superimposed with the corresponding perceptual weight coefficients after dynamic redistribution to obtain a comprehensive evaluation score representing human eye perception. The nonlinear penalty function is an exponential gain mapping function with discrete deviation as the independent variable. By performing nonlinear amplification on the negative discrete difference, the index dimension with the lower score obtains a higher visual significance gain, and the sum of the perceptual weight coefficients after weight allocation is a unit value.

8. A multidimensional temporal similarity evaluation system perceived by the human eye, characterized in that, include: The data preprocessing module is used to obtain the real value sequence and predicted value sequence to be evaluated, and to perform benchmark alignment and fluctuation amplitude normalization processing to generate corresponding mapping sequence pairs under a unified observation field. The global morphology analysis module is used to extract waveform geometric features of the mapping sequence pairs in local intervals using the sampling window, and obtain global morphological similarity based on the correlation strength of waveform geometric features in the spatial dimension. The time warping evaluation module is used to establish nonlinear warping paths for mapping sequence pairs and perform exponential mapping on the cumulative cost generated by the path using the fluctuation scale of the mapping sequence pairs to obtain time warping similarity. The feature anchor matching module is used to extract the local extreme points of each sequence in the mapping sequence pair as feature anchors, and obtain the feature matching score based on the offset distance of the mutually matching feature anchors in the time and amplitude dimensions of the mapping sequence pair. The global distribution quantization module is used to extract the statistical moment features and statistical distribution evolution components of the mapped sequence pairs, and quantify the distribution consistency between the mapped sequence pairs in terms of statistical moment features and statistical distribution evolution components to obtain global distribution similarity. The multidimensional perception fusion module is used to fuse global morphological similarity, temporal regularization similarity, feature matching score and global distribution similarity into a comprehensive evaluation score.

9. A multi-dimensional time series similarity evaluation device oriented towards human visual perception, characterized in that, include: At least one controller; and a memory that is communicatively connected to at least one controller; The memory stores instructions that can be executed by at least one controller, which are executed by at least one controller to enable the at least one controller to perform the human eye-perceived multidimensional temporal similarity evaluation method as described in any one of claims 1-7.

10. A computer-readable storage medium storing computer-executable instructions thereon, characterized in that, When the executable instructions are executed by the controller, they implement the multidimensional temporal similarity evaluation method for human eye perception as described in any one of claims 1-7.

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