A visualization method for device remaining useful life prediction model comparison

Abstract

The application discloses a kind of visual methods for equipment remaining useful life prediction model contrast, after obtaining equipment operation dataset, the data obtained are mapped, sample inspection visual mapping, feature analysis visual mapping and life cycle visual mapping by visual channel model performance overview visualization, visual layout is carried out to the visual module of completion mapping and realizes, and carry out interactive design.The method of the application mainly focuses on the difference between model output and actual equipment life, and the model comparison scheme provided can be applied to shallow machine learning and various different deep machine learning models;By effective visual analysis method, construct novel visual view, combined with linkage interaction means, provide joint comparison and analysis of different subjects and different attribute variables, meet the complex analysis requirements when RUL prediction model is compared.

Description

Technical Field

[0001] This invention relates to the field of information visualization and visual analytics, specifically a visualization method for comparing equipment remaining useful life prediction models. Background Technology

[0002] As a key task of failure prediction and health management, predicting Remaining Useful Life (RUL) has long been a hot topic in the industrial equipment manufacturing field. Accurate RUL prediction helps to rationally plan equipment maintenance and replacement, reduce maintenance costs, and avoid production interruptions or safety accidents caused by equipment damage, thereby improving system reliability and safety. Currently, equipment remaining life prediction has been applied in many fields, such as industrial manufacturing, aerospace, and energy, achieving significant results.

[0003] In fault prediction and health management tasks, equipment monitoring datasets consist of time-series operational data from multiple devices from the start of operation until degradation and replacement. The multidimensional features contained within these datasets reflect the health status and fault information of the equipment, serving as key factors in assessing equipment health and remaining service life. For the RUL prediction task using this equipment monitoring data, existing research has developed numerous machine learning models. These models can automatically learn hidden features and patterns in the dataset and use these patterns to make RUL predictions. The successful application of machine learning models depends on two aspects: the model's predictive performance and its adaptability to real-world application scenarios. Current model comparisons typically use statistical index scores as performance metrics. While these metrics measure the overall predictive accuracy of the model, they cannot provide in-depth insights by considering the time-series characteristics of the equipment's operational data. Experts struggle to investigate the predictive performance of different models for equipment at different operational stages.

[0004] Information visualization and visual analytics methods offer new insights for equipment maintenance experts. These methods present data through intuitive graphics, colors, and symbols, helping users intuitively perceive the data information and patterns contained within the view. Furthermore, by combining interactive elements with the view, visual analytics methods serve as a hierarchical tool, helping analysts gain a deeper understanding of the data and thus supporting more accurate decision-making.

[0005] Currently, visualization research for predictive model comparison mainly focuses on specific models and scenarios, making it difficult to transfer to RUL prediction scenarios for model comparison analysis. Existing research pays little attention to performance comparison of models in the context of time series data, failing to combine overall model performance with local errors, thus hindering analysts' confidence in model performance scores. Furthermore, the view designs of existing methods provide limited information, making it difficult to intuitively perceive and compare the data context of time series. Summary of the Invention

[0006] To address the aforementioned issues, this study proposes a visualization method for comparing prediction models for remaining useful life of equipment. This method provides experts with various data visualization techniques and interactive analysis tools, helping them to quickly understand the overall performance of the prediction models and their local predictive performance throughout the equipment's lifecycle. This allows for a deeper understanding and comparative analysis of the prediction models, ultimately leading to the selection of the appropriate model.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0008] A visualization method for comparing equipment remaining useful life prediction models includes the following steps:

[0009] S1: Data Acquisition and Processing

[0010] After obtaining the equipment operation dataset, we construct equipment health indicators and calculate the indicator scores of the operation samples. At the same time, we perform data preprocessing and train multiple candidate machine learning models. Then, we calculate the model performance scores through statistical functions and finally organize the data into structured data to draw a visualization view.

[0011] S2: Visual Mapping

[0012] The data obtained in step S1 is visualized and mapped using a visual channel:

[0013] Based on the model performance overview visualization map, design a model performance overview view, use horizontal bar charts to present the overall performance score of the model; use a set of bar charts and circular codes to present the prediction error and prediction stability of the model in different RUL stages;

[0014] Based on the sample inspection visualization mapping design, the sample inspection view is presented in the basic form of scatter plot, and the state sample data is projected in combination with the glyphs to present the data distribution pattern and model performance.

[0015] The feature analysis view is designed based on the feature analysis visualization mapping. This visualization method consists of glyphs on the left, a set of bar charts at the top, and a parallel coordinate system in the central area. Each coordinate system corresponds to a feature dimension, allowing equipment maintenance experts to view the feature distribution of the set of operating states and check the feature values ​​of each status glyph to analyze the feature differences of different operating states.

[0016] The lifecycle view is designed based on the lifecycle visualization mapping. An area map is used to map the degradation process of the device during its operational lifecycle. A stepped bar chart is used to encode the prediction error of the model on the current operational sample of the device. A mosaic chart at the bottom of the view represents the contribution of each feature to the current prediction.

[0017] S3: Visual Layout and Implementation

[0018] Visualize and lay out the visual modules that have completed mapping in S2:

[0019] In the model performance overview view, the scores of each model indicator are arranged in a tabular format. For each table cell, the scores of each indicator of the model are mapped to a horizontal bar. The set of bars on the right side of the view records the mean prediction error of the model for running samples at different RUL stages. The prediction variance is encoded by a circle below each bar.

[0020] In the sample inspection view, for each state running sample, UMAP is used to reduce the dimensionality of the vector; the state sample glyph encodes the sample RUL data and the model's prediction performance for the current sample. This glyph can well represent the proportion of RUL in the life cycle and the differences in the performance between various models.

[0021] The feature analysis view includes four parts: SHAP feature contribution calculation, overall view layout, feature bar chart implementation, and feature contribution bubble chart implementation.

[0022] In the lifecycle view, each subview uses a horizontal coordinate axis to identify the device's running RUL, and the size of the top area encodes the health status of the device during operation; the prediction errors of each model throughout the lifecycle are arranged sequentially at the bottom of the view;

[0023] S4: Interaction Design

[0024] In the model performance overview view, hovering the mouse over a coding graphic will bring up the specific information of the current coding. When the user clicks on the corresponding element of the relevant model, the model will be selected and entered into the subsequent view analysis. By hovering the mouse over the graphic elements in views such as sample inspection, the system will follow the mouse and pop up a window to display information such as prediction error and remaining lifetime.

[0025] Furthermore, in step S1, the data acquisition and processing specifically includes:

[0026] S11: Acquire equipment operation data, including equipment monitoring data for each run from normal operation to degradation and failure, and clean and integrate the raw data and store it in the database;

[0027] S12: Construct equipment health indicators based on operational data characteristic variables, and calculate health indicator scores for each operational monitoring data;

[0028] S13: Perform sliding time window processing on the dataset to obtain time series information in the dataset, which is used to construct different RUL prediction models;

[0029] S14: Calculate the evaluation index scores of the prediction model based on various model evaluation functions, including the average prediction error RMSE, the quality score of the model prediction results, and the model's explanatory power R² for data variation; the calculation formula is as follows:

[0030]

[0031]

[0032]

[0033] Where n is the number of samples, h i y represents the absolute error between the predicted and actual RUL values ​​for sample i. i f is the true value. i For predicted values, The average of the predicted values;

[0034] S15: Filter and select models and datasets based on the user's data requirements.

[0035] Furthermore, in step S2, the model performance overview visualization mapping specifically involves: mapping the model performance overview view by position, color, and area; arranging the model and various indicators in a tabular format, with each row presenting the performance of a model under each indicator; mapping the prediction model evaluation indicator scores through the horizontal bar chart on the left side of the view; mapping the mean prediction error of the model at each stage of the device lifecycle through the respective bar charts on the right side of the view, with different stages distinguished by different colors; and mapping the variance of the prediction error for relevant samples through the circular area below the bar chart, indicating the model's error stability for predicting that type of sample.

[0036] Furthermore, in step S2, the sample inspection visualization mapping specifically includes:

[0037] Position mapping: The position of each state sample glyph in the view is determined by the dimensionality reduction result of the data. The shorter the distance between two glyphs, the higher the similarity between the two current state samples. The basic information of the running state sample and the performance of the model in the current sample are combined into a glyph unit. A glyph unit consists of two parts, left and right. The left side encodes the remaining service life of the current running state before the device completely fails through an arc. The right side encodes the prediction performance of different models for this sample through multiple sectors. At the same time, a sector background is added to the right side to define the boundary of the sector.

[0038] Color mapping: The arc to the left of the RUL lettering contains white and gray. White indicates the number of runs the device has undergone to reach its current state, and gray indicates how many runs are left before the device completely fails. Different colors are used on the right side of the lettering to distinguish different models.

[0039] Area mapping: In the status glyph, the left and right arcs are distributed in a 2:1 ratio; the area of ​​the gray arc on the left is mapped by the proportion of the RUL to the overall lifetime, while the area of ​​each sector on the right encodes the model performance. The smaller the error between the model's predicted value and the true value, the more accurate the prediction, and the smaller the corresponding sector area.

[0040] Furthermore, in step S2, the feature analysis visualization mapping specifically includes:

[0041] Spatial location mapping: The sample glyphs on the left are evenly distributed vertically to identify the device number, RUL, and prediction performance of each model corresponding to each operating state; parallel coordinate systems are arranged on the right, with each feature corresponding to one coordinate system, and the distance between each coordinate system and the left and right coordinate systems is determined by the comprehensive contribution of the corresponding feature; a bar chart is set at the top of each coordinate system, and the width of the bar chart is consistent with the width occupied by the corresponding coordinate system; the vertical axis of the coordinate system is used to identify the value range of the corresponding feature, and the feature value of each state sample is determined by the focus of the connecting line on the coordinate axis and the center point of the circle;

[0042] Height Mapping: The height of the top bar chart indicates the contribution of the current feature to each model; the zero point of the bar chart's coordinate axis is in the center of the view. When the feature importance is positive, the bar expands upward from the median line; when the feature importance is negative, the bar extends downward from the median line. The greater the height of the bar, the greater the contribution of the feature to the model corresponding to that bar.

[0043] Color mapping: In the top bar chart set, the bar color of each identifying model is consistent with the color of the encoding model prediction performance of the glyph on the left; in the parallel coordinate system, circles are used to indicate the comprehensive contribution of the current feature to the prediction of each state sample, and each circle maintains 20% opacity. When multiple circles overlap, the color will gradually deepen.

[0044] Area mapping: In a parallel coordinate system, the size of a circle indicates the contribution of the corresponding feature to the sample. The size of the circle is limited by the width of the feature.

[0045] Furthermore, in step S2, the lifecycle visualization mapping specifically involves:

[0046] Area mapping: Establish a unified coordinate system for each view module to map the complete life cycle of the device; set the area map at the top of the view to identify the health indicators at each moment, encode the device's operating health level as area size, and present the complete degradation process of the device throughout its life cycle;

[0047] Stepped line chart mapping: The stepped line chart in the lifecycle view is mapped in shape and color: the first-color line maps the prediction error of the model for all running samples of the current device; the second-color line serves as the baseline when the prediction error is 0, helping users quickly perceive the deviation of the first-color line that indicates the prediction error; the third-color line represents the average prediction error of the model for all device samples under this lifecycle background; and the background stripes of the view map the variance of the prediction error of the model for all devices.

[0048] Mosaic Mapping: Position and color mapping of the mosaic map in the lifecycle view: For each running sample at each moment in the lifecycle, there is a column of mosaic blocks. Each block maps different feature attributes from top to bottom. The color maps the contribution of the feature to the current prediction. The first color and the third color represent positive and negative prediction contributions, respectively. The depth of the color corresponds to its contribution level.

[0049] Furthermore, the sample inspection visualization layout and implementation in step S3 specifically includes:

[0050] S311: Implementation of Scatter Projection of State Samples

[0051] After preprocessing the dataset, the devices and their operating states are represented as follows:

[0052] X dt ∈R K ,d=1,2,…,D,t=1,2,…,T (4)

[0053] In the formula: R is the set of real numbers; K is the number of data features; D is the number of devices; T is the device lifecycle length;

[0054] S312: The state operation of each device contains multiple data points. UMAP dimensionality reduction is performed on the state operation samples of each device as follows:

[0055] a) Calculate the distance matrix

[0056] The distance matrix is ​​defined based on Euclidean distance as follows:

[0057]

[0058] In the formula: D ij For data point x i and x jThe Euclidean distance between them; K is the number of data features; x ik For data point x i The kth eigenvalue, x jk Data point x j The kth eigenvalue;

[0059] b): Selecting a neighborhood

[0060] Constructing a graph structure in a low-dimensional space for each data point x i Select the k nearest neighbors as the neighbors, connect them to form a weighted graph; the weight w ij Let represent the distance between data point i and its neighbor j. The weighted graph is viewed as an adjacency graph in a low-dimensional space. By optimizing this adjacency graph, a manifold structure in a high-dimensional space is approximated. The calculation method is as follows:

[0061]

[0062] In the formula, w ij For similarity weights, d ij Let r be the Euclidean distance between two data points. i For the local scale of the data points, σ i This is a hyperparameter used to regulate the decay rate of the weights;

[0063] c) Embedding a high-dimensional graph into a low-dimensional space using optimization methods.

[0064] A loss function is defined to represent the error between the low-dimensional embedding and the high-dimensional graph. This loss function includes binary cross-entropy loss and KL divergence loss. The binary cross-entropy loss preserves the local structure in the high-dimensional graph, while the KL divergence loss preserves the global structure. The binary cross-entropy loss L is expressed as:

[0065]

[0066] In the formula: q ij p represents the similarity between two data points in a low-dimensional embedding. ij The similarity between two data points in a high-dimensional embedding;

[0067] S313: Implementation of State Sample Glossary:

[0068] The left part of the glyph maps RUL to the length of an arc starting from the bottom, and the calculation process is as follows:

[0069]

[0070] In the formula: cArc is the radius of the target arc to be drawn, rul is the current remaining service life, and rul max The total lifetime is represented by tArc, where tArc is the maximum value of the arc.

[0071] The right side of the character uses multiple sectors of varying sizes to map the prediction performance of each model. The calculation process for the sector radius corresponding to each model is as follows:

[0072]

[0073] In the formula: l is the absolute error between the model's predicted value and the actual value, cPos i l is the width of the arc. i tPos represents the absolute error between the model's predicted value and the actual value, tPos represents the maximum width, and zPos represents the minimum width.

[0074] Furthermore, the feature analysis visualization layout and implementation in step S3 are specifically as follows:

[0075] S321: Calculation of SHAP Feature Contribution

[0076] SHAP calculates the average marginal contribution of each feature across various feature combinations, and then sums these averages to obtain the total contribution of each feature.

[0077] S322: Overall Layout

[0078] The formula for calculating the height coordinates of a font label, i.e., the starting height of the font, is as follows:

[0079]

[0080] In the formula: N is the number of currently drawn glyph labels; curHPos g `height` represents the height of the g-th glyph label within the overall drawing area, `endHPos` represents the end height of the overall view, and `startHPos` represents the start height of the overall view. g The height of the g-th glyph label itself;

[0081] The formula for calculating the width of each coordinate axis in a parallel coordinate system is as follows:

[0082]

[0083] In the formula: curWidth k The width of the drawing area for the corresponding bubble of the k-th feature is defined, where minWidth is the minimum drawing width, totalWidth is the global drawing width, and s k For the contribution of the current k-th feature, s j Let K be the contribution of the j-th feature, and K be the number of data features.

[0084] S323: Implementation of Feature Histogram

[0085] For each feature, calculate the feature contribution O. k The sign of the characteristic contribution determines the direction of the bar chart expansion; the formula is as follows:

[0086]

[0087] In the formula, n is the number of samples, s ki The contribution of the model to the k-th feature on sample i, where K is the number of data features;

[0088] S324: Implementation of Bubble Chart for Feature Contributions

[0089] For a given feature, the size of the loaded bubble is calculated as follows:

[0090]

[0091] In the formula, cRadius b Let a be the loading bubble radius of the b-th model. b denoted as , where C is the size of the container area, A is the total area of ​​the bubbles, and m is the number of models.

[0092] Compared with the prior art, the beneficial effects of the present invention are:

[0093] 1) In response to the lack of model comparisons for RUL prediction scenarios and the lack of model performance comparisons for time-series data characteristics in existing studies, the method of this invention provides an in-depth comparison scheme for RUL prediction model performance based on equipment operation monitoring data, while also paying attention to the time-series characteristics of equipment lifecycle, which improves the effectiveness and practicality of the analysis to a certain extent.

[0094] 2) To address the limitation of model types in existing model visualization research, the method of this invention mainly focuses on the difference between model output and actual equipment lifespan. The model comparison scheme provided by this method can be applied to shallow machine learning and various deep machine learning models.

[0095] 3) To address the shortcomings of multivariate time series data visualization, such as relatively simple encoding schemes, limited visualization views, and limited visual information, the method of this invention constructs novel visualization views through effective visual analysis methods and combines interactive means to provide joint comparative analysis of different subjects and different attribute variables, meeting the complex analysis needs when comparing RUL prediction models. Attached Figure Description

[0096] Figure 1 This is a schematic diagram of a visualization method framework for comparing models for predicting the remaining useful life of equipment.

[0097] Figure 2This is a schematic diagram of the visual encoding and visualization layout in the model performance overview view of this invention.

[0098] Figure 3 This is a schematic diagram of the visual encoding and visualization layout in the sample inspection view of the present invention.

[0099] Figure 4 This is a schematic diagram of the visual encoding and visualization layout in the feature analysis view of the present invention.

[0100] Figure 5 This is a schematic diagram of the visual encoding and visualization layout in the lifecycle view of this invention. Detailed Implementation

[0101] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0102] This invention utilizes a novel visualization design, combined with a multi-view linkage strategy, to implement a comparative visualization method for RUL prediction models based on the device lifecycle. The method includes: data acquisition and processing, visualization mapping, visualization layout and implementation, and interaction design, as detailed below:

[0103] I. Data Acquisition and Preprocessing

[0104] 1) Obtain equipment operation data

[0105] The equipment monitoring sensors are used to monitor the equipment's operating status data, including monitoring data throughout the entire lifecycle from the time the equipment is running until it fails. The raw data is then cleaned, integrated, and stored in a database.

[0106] 2) Construction of health indicators

[0107] Equipment health indicators are constructed based on the characteristic variables of the operational data, and health indicator scores are calculated for each operational monitoring data.

[0108] In RUL prediction studies, many experts assess equipment condition by constructing interpretable health indicators, helping domain experts analyze equipment degradation trends and classify degradation stages. A health indicator suitable for engines, constructed based on operational data characteristic variables, is shown in the following formula:

[0109]

[0110]

[0111] Where T1 is the length of the engine's HI (health index) curve, and F t F is a characteristic of the t-th life cycle. endThis is an engine failure characteristic. During the construction process, the health index HI takes a value of 0 to represent a complete engine failure and 1 to represent a completely normal engine. Therefore, the degradation state of HI is updated and restricted to the range [0,1] using equation (2). HI and HI′ are the HI values ​​before and after the update, respectively. max HI min These are the maximum and minimum values ​​of HI, respectively.

[0112] 3) Sliding time window processing

[0113] A sliding time window is applied to the dataset to obtain time series information, which is then used to construct different RUL prediction models.

[0114] Compared to data sampled at a single time step, the sliding time window method can obtain more temporal information. This temporal information is used as sequence samples to input into models such as RNN and LSTM, enabling the model to learn the temporal dependencies of the data, thereby improving the accuracy of the model's RUL prediction and its generalization performance.

[0115] For a multi-sensor time series of length T, using a time window of size w to slide one time step along the time axis to segment the input data can yield n-w+1 time windows. The longer the time window, the more device state information it contains, but the greater the computational cost, and the sequence trend information embedded across multiple time steps is difficult to learn. It's important to note that the training samples are constructed using a sliding window approach; therefore, each training sample is no longer a single device's operational state, but rather device operational state data over a period of time, with overlapping sensor parameters between adjacent samples.

[0116]

[0117] The calculation method is as shown in equation (3), X d Window data after device d conversion, x i Let s be the window data at time i. i Let be the sensor data at time i; D be the number of devices; w be the time window length; and T be the device lifecycle length. In this embodiment, the time window length is selected as 30, which is an optimized setting.

[0118] 4) Model evaluation function

[0119] Calculate the model evaluation index score based on various model evaluation functions.

[0120] The overall performance of RUL prediction models can be evaluated using various statistical metrics, three commonly used being RMSE, Score, and R². These metrics represent the average prediction error, the quality of the model's predictions, and the model's explanatory power for data variations, respectively. When comparing models in practice, multiple evaluation metrics should be considered comprehensively, taking into account the context and needs of the actual problem to make a reasonable assessment and decision.

[0121] RMSE: In numerous model evaluations, including RUL prediction, RMSE is widely used as a statistical measure for model evaluation and comparison. It represents the root mean square error between the model's predicted value and the actual value.

[0122]

[0123] In the above formula, n is the number of samples. For sample i, h i RMSE is the absolute error between the predicted and actual RUL. RMSE does not distinguish whether the predicted result is less than or greater than the actual RUL; that is, it treats the impact of the model overestimating or underestimating the remaining lifetime equally.

[0124] Score: The formula for calculating the score is as follows:

[0125]

[0126] In the Score evaluation method, the prediction error h i Whether it is less than 0 was discussed separately, when h i When e is less than 0, the denominator of the exponent is 13; when h... i When the value of e is greater than 0, the denominator of the exponent is 10. This means that when the model overestimates the remaining lifespan of the equipment, it will face a greater "penalty" than when the model's predicted value is less than the actual RUL.

[0127] R²: R² (R-squared) is a statistic used to evaluate the goodness of fit of a regression model. It represents the ratio of the variance of the actual data to the variance of the model fit. The value of R² ranges from 0 to 1. If the value is close to 0, it indicates that the model performance is very poor, and the user should consider other models. Conversely, if the value is close to 1, it indicates that the model performance is good, and the model is worth paying attention to and considering.

[0128]

[0129] II. Visual Mapping

[0130] 1) Model performance overview view visualization mapping

[0131] The model performance overview visualization mapping is as follows: the model performance overview view is mapped by position, color, and area; models and various indicators are arranged in a tabular format, with each row showing the performance of a model under each indicator; the evaluation indicator scores of the prediction model are mapped through the horizontal bar chart on the left side of the view; the mean prediction error of the model at each stage of the device lifecycle is mapped through the individual bar charts on the right side of the view, with different stages distinguished by different colors; the variance of the prediction error under relevant samples is mapped through the circular area below the bar chart, indicating the stability of the model's error in predicting that type of sample.

[0132] like Figure 2 As shown, the performance overview view includes three statistical indicator modules: Score, RMSE, and R2, as well as a Deviation module that provides an overview of model performance across the lifecycle stages. The performance elements of each model indicator in the view are arranged in a tabular format, with each model being analyzed arranged row by row, and each row including the score for each performance indicator. The width of the blue bars encodes the statistical indicator score; higher scores are indicated by wider bars. On the right side of this view, several sub-view modules are used to present the prediction errors of each model across the equipment lifecycle stages. The equipment lifecycle is divided into five stages according to RUL: 0-40, 40-90, 90-140, 140-200, and 200-311. The bars above this module represent the mean prediction error of the model for the state samples in that stage; the height of the bar is proportional to the error, and the area of ​​the circle below the module is proportional to the variance of the prediction error. The view shows that as the equipment stage approaches failure, the model's prediction error becomes smaller and more stable. At the same time, when users hover their mouse over the encoded element, a tooltip will display the specific value being encoded.

[0133] 2) Sample inspection visualization mapping

[0134] like Figure 3 As shown, this method uses the basic form of a scatter plot and combines it with a glyph combination to project the state sample data in order to present the data distribution pattern and model performance.

[0135] The scatter plot uses UMAP for dimensionality reduction. Each glyph unit consists of two parts: the left side encodes the remaining lifespan before complete device failure using arcs, while the right side uses multiple sectors to encode the prediction performance of different models for that sample. Specifically:

[0136] Position: The position of each state sample glyph in the view is determined by the dimensionality reduction result of the data. The shorter the distance between two glyphs, the higher the similarity between the two current state samples. This invention integrates the basic information of the running state sample with the model's performance on the current sample into a glyph unit. A glyph unit consists of two parts: the left side encodes the remaining lifespan of the current running state before complete device failure using arcs, while the right side uses multiple sectors to encode the prediction performance of different models for that sample. Simultaneously, a sector background is added to the right side to define the boundaries of the sectors.

[0137] Color: The arc to the left of the RUL lettering contains white and gray. White indicates the number of operations the device has undergone to reach its current state, while gray indicates how many operations remain before the device completely fails. The right side of the lettering uses different colors to distinguish different models. All lettering in the view uses a unified color coding scheme, meaning that equipment maintenance personnel can quickly identify the model corresponding to a color.

[0138] Area: In the status glyph, the left and right arcs maintain a 2:1 ratio. The area of ​​the gray arc on the left is mapped to the proportion of the RUL to the overall lifetime, while the size of each sector on the right encodes the model performance. The smaller the error between the model's predicted value and the true value, the more accurate the prediction, and the smaller the corresponding sector area.

[0139] 3) Feature analysis visualization mapping

[0140] The feature analysis visualization view is designed based on feature analysis visualization mapping. This visualization method consists of glyphs on the left, a set of bar charts at the top, and a parallel coordinate system in the central area. Each coordinate system corresponds to a feature dimension. Equipment maintenance experts can view the feature distribution of the set of operating states, examine the feature values ​​of each status glyph, and analyze the feature differences between different operating states.

[0141] The device number, RUL, and prediction performance of each model are identified on the left-hand sample glyphs in a vertically uniform distribution. In the parallel coordinate system, the coordinate system corresponding to each feature has its distance from the left and right coordinate systems determined by the overall contribution of the corresponding feature. As the distance between a coordinate system and its adjacent coordinate systems increases, the space occupied by that coordinate system also increases, indicating that the current feature contributes more to the prediction. For example... Figure 4 As shown, the mapping encoding of this method includes modules such as spatial location, height, color, and area.

[0142] Spatial Location: The sample characters on the left are evenly distributed vertically, each indicating the device number, RUL, and prediction performance of each model corresponding to its operating state. In the parallel coordinate system, the coordinate systems corresponding to each feature are not evenly distributed. The distance between each coordinate system and the two coordinate systems to the left and right is determined by the overall contribution of the corresponding feature. The greater the distance between a coordinate system and the left and right coordinate systems, the larger the space occupied by that coordinate system, indicating a higher predictive contribution of the current feature. Similarly, the width of the bar chart at the top of each coordinate system is consistent with the width occupied by that coordinate system. This spatial distribution makes important feature information easier for users to perceive and explore. In addition, the vertical axis of each coordinate system indicates the value range of that feature, and the feature values ​​of each state sample are determined by the focus of the connecting lines on the coordinate axes and the center point of the circle.

[0143] Height: In the top set of bars, each feature corresponds to one bar, and the height of the bar indicates the contribution of the current feature to the model. The zero point of the bar axis is in the center of the view. When the feature importance is positive, the bar expands upwards from the median line; when the feature importance is negative, the bar extends downwards from the median line. The greater the bar height, the greater the feature's contribution to the model corresponding to that bar.

[0144] Color: In the top histogram set, the color of each bar representing the model is consistent with the color of the encoding model's prediction performance for the glyphs on the left. In the parallel coordinate system, each circle represents the combined contribution of the current feature to predicting each state sample, and each circle maintains 20% opacity. When multiple circles overlap, the color gradually darkens. The closer the color of a circle in a feature coordinate system is to opaque, the more similar the feature values ​​of multiple samples are.

[0145] Area: The size of the circle in the parallel coordinate system indicates the contribution of the feature to the samples. The size of the circle is limited by the width of the feature. When multiple large circles are in a coordinate system, it indicates that the feature corresponding to that coordinate system has a high contribution value to multiple samples.

[0146] 4) Lifecycle visualization mapping

[0147] The lifecycle view is designed based on the lifecycle visualization mapping. An area map is used to map the degradation process of the device during its operational lifecycle. A stepped bar chart is used to encode the prediction error of the model on the current operational sample of the device. The mosaic chart below the view represents the contribution of each feature to the current prediction.

[0148] like Figure 5As shown, the current visualization method is divided into two parts: the top part encodes the degradation process of device health indicators, and each sub-module below represents the predictive performance of a model and its corresponding feature contribution. All view sub-modules are horizontally laid out, showing the gradual decrease in remaining lifetime from left to right.

[0149] Area: The area graph at the top of the view displays health metrics at each moment. As the graph shows, when the device approaches failure, the health metrics approach 0, and the view area decreases. Through this area graph, users can gain insight into the timing patterns of operational status and the device's degradation process, as well as identify lifecycle moments with abnormal operational status fluctuations.

[0150] Stepped Line Chart: Each model module includes two parts: performance and feature contribution. The blue stepped line chart presents the error between the model's predicted RUL and the actual RUL for each running state. A gray auxiliary line is in the center of the chart, with the gray straight line representing the baseline when the prediction error is 0. This helps users quickly perceive the deviation of the blue line indicating the prediction error. When the stepped line is below this auxiliary line, it means that the model predicts the current running state will enter the failure state faster than it actually will. The line chart also includes a red prediction mean line. The value of each point represents the average predicted value of the model for all devices under the current actual RUL. The red line represents the average prediction error of the model for all device samples in this lifecycle context. For example, the height of the last red line indicates the average prediction error of the model for samples just before all devices fail. In addition, each scale on the horizontal axis has a background band. The color of this band encodes the variance of the model's prediction value. The color is a mid-tone between gray and white. The closer the color is to white, the larger the variance; the darker the color, the smaller the variance and the more stable the prediction value. By observing the temporal changes of the red mean line and the gray-white background stripes, the predictive time series patterns of the model can be analyzed, including fluctuations in accuracy and stability.

[0151] Mosaic Plot: Below the blue ladder plot providing model performance information is a mosaic plot. Each row of this plot corresponds to a feature value, while the horizontal axis still corresponds to the operating states throughout the device's lifecycle. Below each operating state are mosaic rectangles corresponding to each feature value. The color of the rectangle encodes the feature's contribution: the closer the color is to white, the smaller the feature's contribution; the closer the color is to blue, the larger the positive contribution the feature makes to the model's prediction; otherwise, the closer the color is to red, the larger the negative contribution the feature has.

[0152] III. Visual Layout Implementation

[0153] 1. Sample inspection visualization layout and implementation

[0154] 1) Implementation of scattered projection of state samples:

[0155] After preprocessing the dataset, the device and its operating status can be represented as:

[0156] X dt ∈R K ,d=1,2,…,D,t=1,2,…,T (7)

[0157] In the formula: R is the set of real numbers; K is the number of data features; D is the number of devices; T is the device lifecycle length.

[0158] 2) Run sample x for each state. i Using UMAP to reduce the dimensionality of vectors can preserve the global and local structure of the dataset and effectively capture information such as categories, manifold structure and outliers in the data.

[0159] The steps are as follows:

[0160] a) Calculate the distance matrix; UMAP supports calculating the distance matrix using different distance metrics, the most commonly used being Euclidean distance, defined as follows:

[0161]

[0162] In the formula: D ij For data point x i and x j The Euclidean distance between them; K is the number of data features; x ik For data point x i The kth eigenvalue, x jk Data point x j The kth eigenvalue.

[0163] b) Select a neighborhood; construct a graphical structure in low-dimensional space to approximate the manifold structure in high-dimensional space. For each data point x i We can choose a set of k nearest neighbors as neighbors, connect them to form a weighted graph. The weight is w. ij The weighted graph represents the distance between data point i and its neighbor j. This weighted graph can be viewed as an adjacency graph in a low-dimensional space. UMAP optimizes this adjacency graph so that it can approximate a manifold structure in a high-dimensional space. The calculation method is as follows:

[0164]

[0165] c) Embedding high-dimensional graphs into low-dimensional spaces using optimization methods; optimization methods such as stochastic gradient descent (SGD) embed high-dimensional graphs into low-dimensional spaces. During optimization, the objective is to minimize the distance difference between the high-dimensional and low-dimensional representations while preserving the dataset structure as much as possible. To optimize the low-dimensional embedding, a loss function is defined to represent the error between the low-dimensional embedding and the high-dimensional graph. This loss function consists of two parts: binary cross-entropy loss and KL divergence loss. The binary cross-entropy loss preserves the local structure in the high-dimensional graph, while the KL divergence loss preserves the global structure. Specifically, the binary cross-entropy loss can be expressed as:

[0166]

[0167] In the formula: q ij For low-dimensional embedding in y i and y j Similarity between them; p ij For high-dimensional embedding in y i and y j The similarity between them.

[0168] 3) Implementation of state sample glyphs:

[0169] The glyph consists of two parts, left and right. The left part maps the RUL to the length of an arc starting from the bottom. The calculation process is as follows:

[0170]

[0171] The right side uses multiple sectors of varying sizes to map the prediction performance of each model. The calculation process for the sector radius corresponding to each model is as follows:

[0172]

[0173] In the formula: l is the absolute error between the model's predicted value and the actual value, cPos i l is the width of the arc. i tPos represents the absolute error between the model's predicted value and the actual value, tPos represents the maximum width, and zPos represents the minimum width.

[0174] 2. Feature Analysis Visualization Layout and Implementation

[0175] This visualization method consists of four parts: SHAP feature contribution calculation, overall layout, feature bar chart implementation, and feature contribution bubble chart implementation.

[0176] 1) SHAP feature contribution calculation:

[0177] SHAP calculates the contribution of each feature by solving for the Shapley value, that is, the degree of influence of the feature on the output. Specifically, SHAP calculates the average marginal contribution of each feature across various feature combinations, and then sums these averages to obtain the total contribution of each feature. For a given instance, the calculation process can be divided into the following steps:

[0178] Step a1: Select a reference point. This reference point can be the mean or median of the entire dataset, or it can be other specific data points.

[0179] Step a2: Select a kernel function. This kernel function measures the distance between data points and a reference point and calculates the corresponding weights. Commonly used kernel functions include the Gaussian kernel function and the Laplace kernel function.

[0180] Step a3: For a sample i to be explained, calculate its distance to the reference point and calculate the corresponding weight based on the kernel function. Specifically, the distance d can be calculated. i =||x i -x ref ||, with a weight of w i =K(d) i ).

[0181] Step a4: Randomly sample some points from the dataset as the background set, and calculate the distance between each point and the reference point, as well as the corresponding weight. Assume we sampled m data points, which are x1, x2, ..., x... m The distances between them and the reference point are d1, d2, ..., d, respectively. m The corresponding weights are w1, w2, ..., w m .

[0182] Step a5: Calculate the contribution of each feature based on its weight. Specifically, we calculate the contribution of each feature j separately. This indicates that feature j is a pair of samples x. i The contribution level. The calculation formula is as follows:

[0183]

[0184] Step a6: Calculate the total contribution of each feature. Specifically, we calculate the average contribution of each feature to all samples. The calculation formula is as follows:

[0185]

[0186] 2) Overall layout:

[0187] It mainly includes glyph labels on the left, an improved parallel coordinate system view on the right, and a bar chart at the top.

[0188] Font labels. Each font label on the left corresponds to a running state sample. They are evenly arranged in containers at the same height in a parallel coordinate system, and each font has its own height. The drawn height coordinates represent the starting height of that font. The calculation formula is as follows:

[0189]

[0190] In the formula: N is the number of glyph labels currently being drawn; for the g-th glyph label, height g The height of the font label, curHPos g `endHPos` is the height of the glyph label within the overall drawing area, `endHPos` is the end height position of the overall view, and `startHPos` is the start height position of the overall view.

[0191] Parallel coordinate system: In this parallel coordinate system, the width of each coordinate axis is determined by the overall contribution of that feature attribute. To avoid some coordinate axes being too narrow and increasing the user's cognitive burden, a minimum width minHeight = 20 is set. The calculation formula is as follows:

[0192]

[0193] In the formula: curWidth k The width of the drawing area for the corresponding bubble of the k-th feature is defined, where minWidth is the minimum drawing width, totalWidth is the global drawing width, and s k For the contribution of the current k-th feature, s j Let K be the contribution of the j-th feature, and K be the number of data features.

[0194] The width of this coordinate axis determines both the width of the histogram container corresponding to the top of the feature and the maximum width of the feature circle in the coordinate system. Taking the histogram container as an example, the starting coordinates of the container are calculated as follows:

[0195]

[0196] In the formula: curWPos u Let curWidth be the starting position of the u-th bubble. v The width of the preceding bubble.

[0197] 3) Implementation of Feature Bar Chart

[0198] For each feature, there is a feature contribution O. k for:

[0199]

[0200] In the formula, n is the number of samples, s ki Let K be the contribution of the model to the k-th feature on sample i, where K is the number of data features.

[0201] When the feature's contribution is positive, the bar expands upwards from the middle; when the feature's contribution is negative, the bar expands downwards from the middle.

[0202]

[0203] In the formula, mHPos represents the baseline position coordinates, pHPos represents the starting position coordinates of the view, nHPos represents the ending position coordinates of the view, and cHPos represents the ending position coordinates of the view. k The coordinates of the plotting position of feature k.

[0204] 4) Implementation of Bubble Chart of Feature Contributions

[0205] When a user hovers the mouse over a sample glyph, the original feature circle will be used as a container to load a feature bubble chart, showing the difference in the contribution of the current feature to multiple models.

[0206] `tRadius` represents the radius of the original feature circle, consistent with the width of the current coordinate axis. Multiple bubbles correspond to different models, mapping the magnitude and direction of feature contributions from multiple models. The size of the loading bubble for a given feature is calculated as follows:

[0207]

[0208] In the formula, cRadius b Let a be the loading bubble radius of the b-th model. b denoted as , where C is the size of the container area, A is the total area of ​​the bubbles, and m is the number of models.

[0209] Meanwhile, the positive or negative value of the current contribution is indicated by a symbol inside the bubble, and the size of the symbol depends on the size of the bubble.

[0210] 3. Lifecycle Visualization Layout and Implementation

[0211] This visualization method uses a unified horizontal coordinate system to standardize time series patterns, encodes health indicators of the running status through area charts, and integrates methods such as stepped line charts and mosaic charts to encode model performance and feature importance information, helping users to explore model performance in depth and make comparisons.

[0212] a) Implementation of health indicator area map

[0213] The horizontal coordinate system of this view encodes the device lifecycle and RUL. Starting from the left coordinate startPos, it represents the initial detection state of the device; as the view expands to the right, the RUL gradually decreases until the rightmost coordinate endPos, at which point the RUL is 0, and the device fails.

[0214]

[0215] Based on the above coordinate system, the health indicators of each device operation determine the height of the current coordinate point. Connecting all coordinate points and filling the area between them and the coordinate axes forms a one-sided area map. To enhance the user's perception of timing patterns and quickly identify abnormal device degradation state samples, this method also draws a similar one-sided area map on the other side of the coordinate axis and merges the two graphs to form a symmetrical area map.

[0216] b) Implementation of model performance time series diagram

[0217] The model performance time series diagram consists of two parts: the performance module and the feature module, which respectively map the model's time series performance error and the contribution of multiple features at each time step.

[0218] Performance module: Both the blue stepped line graph and the red line graph indicate the error, while the gray dashed line encodes the origin of the coordinates as a reference.

[0219]

[0220]

[0221] Among them, the blue broken line encoded data w rul The red line represents the RUL prediction result of the current model, encoding the data w. rul This is the average of the RUL prediction results for all models.

[0222] In addition, each RUL time step of this module has a background color for encoding variance. The color mapping scheme normalizes the data and encodes it using a linear scale where white is 0 and gray-black is 1.

[0223] The specific calculation method is as follows:

[0224]

[0225]

[0226] Feature Contribution Module: Feature contribution still provides good explanation for the time-series patterns predicted by the model. Each row in this module represents the contribution of a feature, and its color coding scheme is similar to... Figure 5Similar. Due to the positive and negative characteristics of feature contribution, this color coding scheme considers two cases: when the feature contribution is positive, color... min The color is coded as 0. max The maximum value of the contribution of the blue coding feature; when the contribution of this feature is negative, color min The color code remains 0, still white. max The minimum contribution to the red coding feature.

[0227] IV. Interaction Design

[0228] In the model performance overview view, hovering the mouse over a coding graphic will bring up the specific information of the current coding. When the user clicks on the corresponding element of the relevant model, the model will be selected and entered into the subsequent view analysis. By hovering the mouse over the graphic elements in views such as sample inspection, the system will follow the mouse and pop up a window to display information such as prediction error and remaining lifetime.

Claims

1. A visualization method for comparing equipment remaining useful life prediction models, characterized in that, Includes the following steps: S1: Data Acquisition and Processing After obtaining the equipment operation dataset, we construct equipment health indicators and calculate the indicator scores of the operation samples. At the same time, we perform data preprocessing and train multiple candidate machine learning models. Then, we calculate the model performance scores through statistical functions and finally organize the data into structured data to draw a visualization view. S2: Visual Mapping The data obtained in step S1 is visualized and mapped using a visual channel: Based on the model performance overview visualization map, design a model performance overview view, use horizontal bar charts to present the overall performance score of the model; use a set of bar charts and circular codes to present the prediction error and prediction stability of the model in different RUL stages; Based on the sample inspection visualization mapping design, the sample inspection view is presented in the basic form of scatter plot, and the state sample data is projected in combination with the glyphs to present the data distribution pattern and model performance. The feature analysis view is designed based on the feature analysis visualization mapping. This visualization method consists of glyphs on the left, a set of bar charts at the top, and a parallel coordinate system in the central area. Each coordinate system corresponds to a feature dimension, allowing equipment maintenance experts to view the feature distribution of the set of operating states and check the feature values ​​of each status glyph to analyze the feature differences of different operating states. The lifecycle view is designed based on the lifecycle visualization mapping. An area map is used to map the degradation process of the device during its operational lifecycle. A stepped bar chart is used to encode the prediction error of the model on the current operational sample of the device. A mosaic chart at the bottom of the view represents the contribution of each feature to the current prediction. S3: Visual Layout and Implementation Visualize and lay out the visual modules that have completed mapping in S2: In the model performance overview view, the scores of each model indicator are arranged in a tabular format. For each table cell, the scores of each indicator of the model are mapped to a horizontal bar. The set of bars on the right side of the view records the mean prediction error of the model for running samples at different RUL stages. The prediction variance is encoded by a circle below each bar. In the sample inspection view, for each state running sample, UMAP is used to reduce the dimensionality of the vector; the state sample glyph encodes the sample RUL data and the model's prediction performance for the current sample. This glyph can well represent the proportion of RUL in the life cycle and the differences in the performance between various models. The feature analysis view includes four parts: SHAP feature contribution calculation, overall view layout, feature bar chart implementation, and feature contribution bubble chart implementation. In the lifecycle view, each subview uses a horizontal coordinate axis to identify the device's running RUL, and the size of the top area encodes the health status of the device during operation; the prediction errors of each model throughout the lifecycle are arranged sequentially at the bottom of the view; S4: Interaction Design In the model performance overview view, hovering the mouse over a coding graphic will bring up the specific information of the current coding. When the user clicks on the corresponding element of the relevant model, the model will be selected and entered into the subsequent view analysis. By hovering the mouse over the element graphic in the sample inspection view, the system will follow the mouse and pop up a window to display prediction error and remaining lifetime information. In step S2, the sample inspection visualization mapping specifically includes: Position mapping: The position of each state sample glyph in the view is determined by the dimensionality reduction result of the data. The shorter the distance between two glyphs, the higher the similarity between the current two state samples. The basic information of the running state sample and the performance of the model in the current sample are combined into a glyph unit. A glyph unit consists of two parts, left and right. The left side encodes the remaining service life of the current running state before the device completely fails through an arc. The right side encodes the prediction performance of different models for this sample through multiple sectors. At the same time, a sector background is added to the right side to define the boundary of the sector. Color mapping: The arc to the left of the RUL lettering contains white and gray. White indicates the number of runs the device has undergone to reach its current state, and gray indicates how many runs are left before the device completely fails. Different colors are used on the right side of the lettering to distinguish different models. Area mapping: In the status glyph, the left and right arcs are distributed in a 2:1 ratio; the area of ​​the gray arc on the left is mapped by the proportion of the RUL to the overall lifetime, while the area of ​​each sector on the right encodes the model performance. The smaller the error between the model's predicted value and the true value, the more accurate the prediction, and the smaller the corresponding sector area.

2. The visualization method for comparing equipment remaining useful life prediction models according to claim 1, characterized in that, In step S1, the data acquisition and processing specifically includes: S11: Acquire equipment operation data, including equipment monitoring data for each run from normal operation to degradation and failure, and clean and integrate the raw data and store it in the database; S12: Construct equipment health indicators based on operational data characteristic variables, and calculate health indicator scores for each operational monitoring data; S13: Perform sliding time window processing on the dataset to obtain time series information in the dataset, which is used to construct different RUL prediction models; S14: Calculate the evaluation index scores of the prediction model based on various model evaluation functions, including the average prediction error RMSE, the quality score of the model prediction results, and the model's explanatory power R2 for data variations. The calculation formula is as follows: （1）； （2）； （3）； in, For the number of samples, For the sample The absolute error between the predicted and actual RUL values; For the true value, For predicted values, The average of the predicted values; S15: Filter and select models and datasets based on the user's data requirements.

3. The visualization method for comparing equipment remaining useful life prediction models according to claim 2, characterized in that, In step S2, the model performance overview visualization mapping specifically involves mapping the position, color, and area of ​​the model performance overview view; the model and various indicators are arranged in a tabular format, with each row presenting the performance of a model under each indicator; The evaluation scores of the prediction model are mapped to the horizontal bar chart on the left side of the view; the mean prediction error of the model at each stage of the device lifecycle is mapped to the individual bars on the right side of the view, with different colors used to distinguish different stages; the variance of the prediction error for relevant samples is mapped to the circular area below the bars, indicating the stability of the model's error in predicting that type of sample.

4. The visualization method for comparing equipment remaining useful life prediction models according to claim 1, characterized in that, In step S2, the feature analysis visualization mapping specifically includes: Spatial location mapping: The sample glyphs on the left are evenly distributed vertically to identify the device number, RUL, and prediction performance of each model corresponding to each operating state; parallel coordinate systems are arranged on the right, with each feature corresponding to one coordinate system, and the distance between each coordinate system and the left and right coordinate systems is determined by the comprehensive contribution of the corresponding feature; a bar chart is set at the top of each coordinate system, and the width of the bar chart is consistent with the width occupied by the corresponding coordinate system; the vertical axis of the coordinate system is used to identify the value range of the corresponding feature, and the feature value of each state sample is determined by the focus of the connecting line on the coordinate axis and the center point of the circle; Height Mapping: The height of the top bar chart indicates the contribution of the current feature to each model; the zero point of the bar chart's coordinate axis is in the center of the view. When the feature importance is positive, the bar expands upward from the median line; when the feature importance is negative, the bar extends downward from the median line. The greater the height of the bar, the greater the contribution of the feature to the model corresponding to that bar. Color mapping: In the top bar chart set, the bar color of each identifying model is consistent with the color of the encoding model prediction performance of the glyph on the left; in the parallel coordinate system, circles are used to indicate the comprehensive contribution of the current feature to the prediction of each state sample, and each circle maintains 20% opacity. When multiple circles overlap, the color will gradually deepen. Area mapping: In a parallel coordinate system, the size of a circle indicates the contribution of the corresponding feature to the sample. The size of the circle is limited by the width of the feature.

5. The visualization method for comparing equipment remaining useful life prediction models according to claim 1, characterized in that, In step S2, the lifecycle visualization mapping is specifically as follows: Area mapping: Establish a unified coordinate system for each view module to map the complete life cycle of the device; set the area map at the top of the view to identify the health indicators at each moment, encode the device's operating health level as area size, and present the complete degradation process of the device throughout its life cycle; Stepped line chart mapping: Shape and color mapping of the stepped line chart in the lifecycle view: The first color line maps the prediction error of the model for all running samples of the current device; the second color line is used as the baseline when the prediction error is 0, helping users to quickly perceive the degree of deviation of the first color line that indicates the prediction error. The third-color line represents the average prediction error of the model for all device samples in this lifecycle context; the background stripes of the view represent the variance of the prediction error of the model for all devices. Mosaic Mapping: Position and color mapping of the mosaic map in the lifecycle view: For each running sample at each moment in the lifecycle, there is a column of mosaic blocks. Each block maps different feature attributes from top to bottom. The color maps the contribution of the feature to the current prediction. The first color and the third color represent positive and negative prediction contributions, respectively. The depth of the color corresponds to its contribution level.

6. The visualization method for comparing equipment remaining useful life prediction models according to claim 1, characterized in that, The sample inspection visualization layout and implementation in step S3 specifically include: S311: Implementation of Scatter Projection of State Samples After preprocessing the dataset, the devices and their operating states are represented as follows: （4）； In the formula: R is the set of real numbers; K is the number of data features; D is the number of devices; T is the device lifecycle length; S312: The state operation of each device contains multiple data points. UMAP dimensionality reduction is performed on the state operation samples of each device as follows: a) Calculate the distance matrix The distance matrix is ​​defined based on Euclidean distance as follows: （5）； In the formula: For data points and The Euclidean distance between them; K is the number of data features; For data points The kth eigenvalue, Data points The kth eigenvalue; b): Selecting a neighborhood Constructing a graph structure in low-dimensional space for each data point Select the most recent set Each neighboring node is considered a neighbor, and they are connected to form a weighted graph; weights Representing data points and his neighbors The distance between them is used to treat the weighted graph as an adjacency graph in a low-dimensional space; by optimizing this adjacency graph, a manifold structure in a high-dimensional space is approximated; the calculation method is as follows: （6）； In the formula, For similarity weights, Let Euclidean distance be the distance between two data points. For the local scale of data points, This is a hyperparameter used to regulate the decay rate of the weights; c) Embedding a high-dimensional graph into a low-dimensional space using optimization methods. A loss function is defined to represent the error between the low-dimensional embedding and the high-dimensional graph. This loss function includes binary cross-entropy loss and KL divergence loss. The binary cross-entropy loss preserves the local structure in the high-dimensional graph, while the KL divergence loss preserves the global structure. The binary cross-entropy loss L is expressed as: （7）； In the formula: The similarity between two data points in a low-dimensional embedding; The similarity between two data points in a high-dimensional embedding; S313: Implementation of State Sample Glossary: The left part of the glyph maps RUL to the length of an arc starting from the bottom, and the calculation process is as follows: （8）； In the formula: Let the radius of the target arc to be drawn be . For the current remaining useful life, For total lifespan, The maximum value of the arc; The right side of the character uses multiple sectors of varying sizes to map the prediction performance of each model. The calculation process for the sector radius corresponding to each model is as follows: （9）； In the formula: The absolute error between the model's predicted value and the actual value. The width of the arc. The absolute error between the model's predicted value and the actual value. For the maximum width, This is the minimum width.

7. The visualization method for comparing equipment remaining useful life prediction models according to claim 1, characterized in that, The feature analysis visualization layout and implementation in step S3 are as follows: S321: Calculation of SHAP Feature Contribution SHAP calculates the average marginal contribution of each feature across various feature combinations, and then sums these averages to obtain the total contribution of each feature. S322: Overall Layout The formula for calculating the height coordinates of a font label, i.e., the starting height of the font, is as follows: （10）； In the formula: The number of glyph labels currently being drawn; For the first The height of the character-shaped label within the overall drawing area This is the end height of the overall view. This is the starting height for the overall view. For the first The height of the character-shaped label itself; The formula for calculating the width of each coordinate axis in a parallel coordinate system is as follows: （11）； In the formula: The width of the drawing area for the corresponding bubble is drawn for the k-th feature. Minimum drawing width, Draw the width globally. The contribution of the current k-th feature. The contribution of the j-th feature, The number of data features; S323: Implementation of Feature Histogram For each feature, calculate the feature contribution. The sign of the characteristic contribution determines the direction of the bar chart expansion; the formula is as follows: （12）； In the formula, For the number of samples, For the model on sample i, the first The contribution of features The number of data features; S324: Implementation of Bubble Chart for Feature Contributions For a given feature, the size of the loaded bubble is calculated as follows: （13）； In the formula, For the first The loading bubble radius of each model, For the current features of the model Contribution For the area of ​​the container, This represents the total area of ​​the bubbles. This represents the number of models.

Images