Material supplement analysis system and method based on least square method and DeltaV system

Abstract

The invention provides a material supplement analysis system and method based on a least square method and a DeltaV system. The system comprises a product library management module, a data interface module, a curve fitting module, a deviation calculation module, a supplement amount calculation module and a man-machine interaction module. The core of the method is that the curve fitting module carries out polynomial fitting for 1-9 times by adopting a least square method, and evaluates the fitting quality according to a decision coefficient R2; the system also has a fitting strategy switching function, and when R2 is lower than a dynamically adjusted threshold value, a linear function or a local weighted regression strategy can be switched; the supplement amount calculation module has a self-learning capability, and can optimize the model and recommend a scheme according to historical data; the system is further integrated with a predictive analysis module for trend early warning, and closed-loop automatic control can be achieved through a special control block in DeltaV. According to the invention, the crossing of material supplement from auxiliary calculation to intelligent decision making and execution is realized, and the production precision and the automation level are obviously improved.

Description

Technical Field

[0001] This invention belongs to the field of industrial process control and automation technology, and in particular relates to a material replenishment analysis system and method based on the least squares method and DeltaV system. Background Technology

[0002] In continuous production processes such as chemical and pharmaceutical manufacturing, it is often necessary to sample and test intermediate products, and then add materials based on the test results to adjust product properties (such as viscosity and acid value) to meet final standards. Traditional methods rely on operator experience, determining the amount to add through table lookups or simple calculations. This method suffers from high subjectivity, low accuracy, and slow response.

[0003] In existing technologies, some systems employ algorithms for process optimization. For example, some patents use the least squares method for material proportioning control, but this is usually an independent optimization module with low integration with the underlying control system (such as DeltaV) and the upper-level information system (such as MES), making it difficult to form closed-loop control. Furthermore, these systems suffer from insufficient fitting accuracy when facing complex nonlinear processes and lack effective fitting quality assessment and backup mechanisms. When the fitting effect is poor, the system reliability decreases significantly.

[0004] DeltaV is a widely used distributed control system (DCS) under Emerson Process Management. While DeltaV offers powerful control capabilities, its native module library lacks control blocks specifically designed for material replenishment scenarios with advanced curve fitting and intelligent decision-making functions.

[0005] Therefore, there is an urgent need in this field for a material replenishment analysis solution that can be seamlessly integrated with existing industrial control systems (such as DeltaV), has high-precision fitting and self-evaluation capabilities, and is flexible in operation. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a material replenishment analysis system and method based on the least squares method and DeltaV system with high accuracy, high integration, high intelligence and high reliability.

[0007] The technical solution disclosed in this invention is specifically implemented as follows: A material replenishment analysis system based on the least squares fitting algorithm and the DeltaV control platform, which mainly includes the following core functional modules: Product Library Management Module: This module uses a visual window form interface, allowing process engineers to easily add, modify, and delete product parameters. Each product's standard curve can have up to 10 standard control points set, and users can customize the numerical range or percentage tolerance band of the upper and lower deviation curves according to actual needs. It can also manage up to 100 different types of supplementary materials. This module has the function of batch importing and exporting product parameters via Excel templates, and is deployed independently outside the factory's core production database, offering high operational flexibility and system adaptability.

[0008] Data Interface Module: This module is based on the standard API interface and OPC unified communication architecture provided by the DeltaV system to achieve stable data communication with the DeltaV control station and MES (Manufacturing Execution System). It can automatically acquire production-related data in real time, including key information such as batch number, product brand and quality sampling values.

[0009] Curve Fitting Module: This module uses the least squares method as its core algorithm and employs Gaussian elimination to solve for polynomial coefficients. It supports various polynomial fitting models from order 1 to 9. The specific implementation steps are as follows: Construct the objective function: for N standard sampling points (x i y i (i=1,2,...,N), using an nth-degree polynomial (1≤n≤9) as the fitting objective function, the expression is: Where a0, a1, ..., a n The coefficients to be determined; Constructing the coefficient matrix and constant term matrix: A system of least squares equations is constructed using the Vandermonde matrix, with the coefficient matrix A = X. T X, constant term matrix b=X T y, where X is an N×(n+1) order Vandermonde matrix (the elements in the i-th row are [1, x). i x i 2 , ..., x i n The augmented matrix [A|b] is transformed into row echelon form by elementary row operations, and the coefficients a0−a are solved by back substitution. n .

[0010] Gaussian elimination solution: Perform elementary row operations on the augmented matrix [A|b] (swapping rows, multiplying a row by a non-zero constant, adding a row to a multiple of another row) to transform it into a row echelon form matrix, and obtain the coefficients a0, a1, ..., an by back substitution; Fit quality assessment: using the coefficient of determination R0 2 The quality of the quantified fit is calculated using the following formula: ,in The fitted value is calculated by substituting it into the objective function. These are measured values. The average of the measured values .

[0011] The core innovation of this module is the introduction of the coefficient of determination R. 2 As a quantitative indicator for evaluating the goodness of curve fitting, a dynamic switching unit for the fitting strategy is designed: when the system detects R... 2 When the value falls below a threshold that is dynamically adjusted based on real-time data, the system can automatically switch to a linear function fitting or a non-parametric locally weighted regression strategy, thereby significantly improving the system's adaptability and robustness under different production conditions.

[0012] Preferably, the fitting strategy switching unit is further configured to automatically adopt a local weighted regression strategy to calculate the bias when the system detects that the real-time sampling data has heteroscedasticity or local nonlinear characteristics.

[0013] The method for detecting heteroscedasticity is as follows: calculate the fitting residual (measured value). with fitted value The sum of squares of the differences between the x-coordinates is used to determine heteroscedasticity. If the sum of squares of the residuals increases (or decreases) by ≥30% as the x-coordinate increases, it is considered that heteroscedasticity exists. The method for detecting the local nonlinear features is as follows: calculate the slope of three adjacent sampling points (k1=(y2-y1) / (x2-x1), k2=(y3-y2) / (x3-x2)), and if |k2-k1| / k1≥20%, it is determined that there are local nonlinear features.

[0014] Deviation Calculation and Supplement Calculation Modules: The deviation calculation unit calculates the quality deviation based on the difference between the actual Y-coordinate value of the sampling point and the predicted Y-value at the same X-coordinate by the currently used strategy (standard fitting curve, linear function, or locally weighted regression line). The supplement calculation unit integrates a self-learning mechanism, which can automatically record key data from historical operations and continuously optimize the supplement calculation model using machine learning methods. When a working condition similar to historical scenarios is detected, it can automatically recommend the optimal supplement plan.

[0015] The initial form of the replenishment calculation model is Q=k×ΔY×M, where: Q is the replenishment amount (unit: kg); ΔY is the Y-axis deviation value output by the deviation calculation module (unit: %, absolute value); M is the current material weight (unit: kg); and k is the material correction coefficient (initial k=1.02 for liquid materials, initial k=0.98 for solid materials). Machine learning employs gradient descent to optimize the value of k: The objective is to achieve a final product deviation ≤ 0.5% after replenishment, with a learning rate of 0.01. The update formula for each iteration is as follows: , where Loss is the squared difference between the actual deviation and the target deviation after the addition, and the iteration stops when Loss≤0.0025.

[0016] Predictive analysis module: This module builds a time series model based on real-time acquired continuous sampling data to predict product quality trends and issue early warning signals before possible exceedances. The sampling period is 5-30 minutes and can be configured through the human-computer interaction module.

[0017] The quantitative standard for triggering an early warning is as follows: when the prediction deviation is greater than or equal to 80% of the acceptable range (upper deviation - lower deviation), or when the predicted value will exceed the acceptable range within the next two sampling periods, the system will trigger an audible and visual alarm and an interface pop-up warning.

[0018] Human-computer interaction module: Provides a graphical user interface that centrally displays all real-time system data, fitted curves, deviation information, supplementation suggestions, and early warning prompts, and receives user operation commands and parameter inputs.

[0019] MRAS Control Block: To convert the replenishment amount output by the replenishment amount calculation module into actual production execution instructions, this system integrates a dedicated MRAS control block within the DeltaV control system. This control block communicates with the replenishment amount calculation module in real time via an internal data bus. After receiving the replenishment amount data, it generates control signals to drive the actuator according to preset rules. The specific implementation is as follows: The control signal uses a 4-20mA standard analog signal, and its mapping relationship with the replenishment amount is linear: when the replenishment amount Q=0kg, the output is 4mA; when the replenishment amount Q=Q max (Q) max The maximum replenishment amount for this material in a single batch is preset by the product library, such as Q for solvent B. max When the weight is 500kg, the output is 20mA; the intermediate replenishment amount is calculated as I=4+16×(Q / Q). max Calculate (I is the output current, unit: mA).

[0020] The system communicates with the DeltaV control station via the OPC UA protocol, with a data transmission cycle of 500ms. The execution status of the feed pump / regulating valve (such as "running / stopping") is fed back to the MRAS control block via DeltaV. If the feedback shows "execution failed", the system triggers an audible and visual alarm and re-outputs the control signal.

[0021] Accordingly, the present invention also provides a material replenishment analysis method based on the above system, specifically including the following steps: S1: Preset product parameters, and create or modify the product's standard curve, upper and lower deviation tolerance curve, and basic information of related supplementary materials through the product library management module; S2: After the production batch starts, the data interface module automatically obtains the batch number and product name of the current batch from the DeltaV system and matches and verifies them with the information stored in the product database. If a match cannot be found, an alarm prompt will be triggered immediately. S3: After a successful match, the system automatically calls the curve fitting module to fit the standard curve of the current product, generates the standard fitting curve and displays it visually in the chart interface of the human-computer interaction module, and draws the upper and lower deviation boundary curves at the same time. S4: Automatically receives real-time sampling data from the quality control system through the data interface module, or allows operators to manually enter sampling point data through the human-machine interface and dynamically draw and display it in the same chart; S5: The deviation calculation module automatically calculates the deviation between the measured values ​​of the sampling points and the standard fitting curve (or the reference line generated by the backup fitting strategy) based on the current fitting strategy. S6: Based on the deviation calculation results or the intelligent recommendation given by the system, the operator selects the type of material to be replenished and enters the current material inventory. The replenishment calculation module automatically calculates the accurate replenishment quantity. S7: The system automatically records the sampling information, deviation calculation results and the final supplementary operation data to an internal array or relational database, and supports exporting all data to an Excel report after the production batch is completed; S8: Based on the output of the predictive analysis module, the system issues early warnings of quality trends or automatically issues control commands through the MRAS control block to execute closed-loop replenishment operations.

[0022] Compared with the prior art, the embodiments of this application have the following main advantages: High precision and intelligence: Prediction accuracy is improved through high-order fitting and determination coefficient evaluation; dynamic thresholds and multi-strategy switching ensure intelligent adaptation under complex working conditions.

[0023] Continuous evolution and experience accumulation: Self-learning and recommendation functions enable the system to accumulate expert experience, continuously optimize itself, and reduce dependence on specific operators.

[0024] Proactive control: The predictive analytics module enables a shift from "post-event correction" to "pre-event prevention," reducing quality fluctuations and scrap rates.

[0025] Deep closed-loop integration: Through a dedicated MRAS control block, it achieves deep coupling with the DeltaV ecosystem and full-process automation of "perception-decision-execution", which is a key step towards a smart factory.

[0026] Flexibility and scalability: The Excel-compatible product library design and independent architecture facilitate deployment and expansion. Attached Figure Description

[0027] Figure 1 This is a flowchart and overview of the method of the system of the present invention.

[0028] Figure 2 This is a schematic diagram of the main software panel interface of the system of the present invention.

[0029] Figure 3 This is a schematic diagram of the product parameter settings window (New / Modify).

[0030] Figure 4 This is a schematic diagram of the MRAS control block parameter list.

[0031] Figure 5 This is a comparison graph of curves under different fitting iterations.

[0032] Figure 6 This is a schematic diagram of the interface for inputting sampling points and displaying the deviation calculation results.

[0033] Figure 7 This is a schematic diagram of the dynamic threshold and local weighted regression strategy in an embodiment of the present invention.

[0034] Figure 8 This is a schematic diagram illustrating the principle of the self-learning and recommendation function in an embodiment of the present invention.

[0035] Figure 9 This is a flowchart illustrating the predictive analysis and closed-loop control in an embodiment of the present invention. Detailed Implementation

[0036] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs; the terminology used herein in the specification of the application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application; the terms "comprising" and "having," and any variations thereof, in the specification, claims, and foregoing drawings of this application are intended to cover non-exclusive inclusion. The terms "first," "second," etc., in the specification, claims, or foregoing drawings of this application are used to distinguish different objects, not to describe a particular order.

[0037] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0038] Example 1 This invention provides a material replenishment analysis method based on a material replenishment analysis system using the least squares method and the DeltaV system, such as... Figure 1 As shown, the preparation phase: engineers through... Figure 3 The settings window shown is for creating a standard curve for the new product "Resin-A". Enter 8 standard sampling points (viscosity, acid value). Since there are fewer than 10, repeat the coordinates of the last two points to fill the gap. Set the upper deviation to "percentage +2%" and the lower deviation to "percentage -2%". In the replenishment material column, pre-select materials such as "Solvent B" and "Curing Agent C".

[0039] Production Start-up: Batch begins. The data interface module retrieves the current product as "Resin-A" from DeltaV. The system successfully matches the product library and then calls the curve fitting module. Initially set to quadratic fitting, the calculated R... 2 The value is 0.965, which is lower than the threshold of 0.98.

[0040] Fitting optimization: Engineers use the human-computer interaction module ( Figure 2 The fitting order is gradually increased to 5, at which point R0 2 The fit quality was rated as "high quality" when it reached 0.992. The chart clearly shows the dark green standard fit curve and the red and blue deviation range bands.

[0041] Sampling and Analysis: The MES system returns the first sampling point (X1, Y1). The deviation calculation module compares this point with the fitted curve, calculates the deviation ΔY1, and displays it on the interface. Figure 6 In the deviation column of )

[0042] Replenishment Decision: Based on the deviation ΔY1, the operator selects "Solvent B" from the drop-down menu and enters the current weight of the material in the vessel as 5000 kg. The replenishment calculation module immediately calculates that 125 kg of "Solvent B" needs to be replenished.

[0043] Data traceability: All data from this operation (sampling points, deviations, replenishment amounts, timestamps) is recorded in the RECORD_ARRAY field of the MRAS control block. After the production batch is completed, the operator exports the complete record to an Excel file for quality traceability and analysis.

[0044] Example 2 In another specific embodiment, for a certain type of product with a high degree of data point dispersion, the system determines its coefficient of determination R after completing nine consecutive data fitting tests under different conditions. 2The fit score was only 0.95, failing to meet the conventionally set high-fit quality standard. Nevertheless, because the system automatically identified that the product was currently in the "early reaction" stage—a stage label derived from the system's multi-dimensional evaluation of the reaction process—the system dynamically adjusted the fit acceptance threshold, moderately relaxing it from the default strict 0.98 to 0.94. Based on this adjustment, the system ultimately maintained the analysis mode of using the fitted function for modeling, without switching to other alternative strategies.

[0045] Meanwhile, during real-time data monitoring, the system discovered that recently collected sample points exhibited a significant clustering pattern within a specific X-axis interval, and the distribution pattern displayed a unique trend (see Appendix for details). Figure 7 To address this local data characteristic, the system automatically initiates a local weighted regression algorithm (e.g., when multiple dense real-time sampling points exist within a certain X-coordinate interval, the system uses a local weighted regression algorithm within that interval, assigning higher weights to neighboring points to generate a regression line that better reflects the local data trend, used for deviation calculation in that area), performing high-density calculations within that interval. Compared to global fitting or simple linear function fitting, this method can more sensitively capture local fluctuations and deviations, thus providing more accurate local numerical estimates. Operators can use the local deviation analysis output by the system to make more detailed and precise adjustments to material replenishment operations, effectively improving the accuracy and response efficiency of process control.

[0046] Example 3 like Figure 8 As shown, the self-learning unit of this system, as one of the core functional modules, runs continuously in the system background, constantly recording and analyzing the complete context information involved in each supplementary operation. The system considers each operation result of "the product finally passes inspection after supplementation" as a successful experience and labels it with a success tag. As the number of operations accumulates, the system gradually builds a structured knowledge base through multiple iterations. This knowledge base stores a large number of operation records and their corresponding result information.

[0047] When the system detects new sampling data, the self-learning unit immediately initiates a calculation process to assess the similarity between the current scenario and various scenarios in the historical records. If the system identifies a historical successful case with a similarity exceeding 90% (the second preset threshold), a prompt message will automatically pop up on the human-computer interaction interface, such as: "A similar historical case has been detected. This case shows that adding XX kg of 'solvent B' will make the final product qualified. The system assesses the success rate of this operation to be approximately 95%." This function provides on-site operators with a reliable basis for decision-making based on historical data, significantly enhancing the accuracy and efficiency of operations.

[0048] Meanwhile, the key coefficient k of the mathematical model used in the system to calculate the replenishment amount—i.e., replenishment amount = k × deviation / current weight—is continuously fine-tuned using a gradient descent optimization algorithm. This process enables the system to continuously approach the optimal replenishment strategy, further improving control accuracy and adaptability.

[0049] The current operating condition is 'deviation 0.82%, solvent B, material weight 5000kg'. The similarity calculation between this condition and the historical case 'deviation 0.85%, solvent B, material weight 4900kg' is: Euclidean distance = √[(0.82-0.85)] 2 ×0.4+(1-1) 2 ×0.3+(1-1) 2 [×0.3]=0.018, similarity=1-0.018=98.2% (>90% threshold), therefore the trigger scheme is recommended.

[0050] Example 4: Predictive Early Warning and Closed-Loop Control like Figure 9 As shown, the predictive analysis module of this system uses time series analysis (linear extrapolation for prediction) to dynamically monitor and model four continuously collected sampling points (P1 to P4) during the production process. When the module determines through its algorithm that the predicted value of the next sampling point (P5) will exceed the preset upper deviation limit, the system will immediately activate the audible and visual alarm and display a prompt message on the operation interface: "The next sampling point is expected to exceed the limit; early intervention is recommended." This early warning mechanism provides operators with a critical processing window, effectively avoiding quality deviations.

[0051] On intelligent production lines equipped with closed-loop control, operators can authorize the system to switch to fully automatic operation mode based on actual conditions. In this mode, the MRAS control block automatically generates a 4-20mA standard analog signal after calculating the required material replenishment amount in real time, and transmits this signal directly to the frequency converter or regulating valve of the replenishment pump. For example, if the calculated replenishment amount Q = 125kg, and the solvent B's Q... max =500kg, substituting into the formula, we get I=4+16×(125 / 500)=8mA. After receiving the 8mA signal, the feed pump operates according to the corresponding flow rate (e.g., 8mA corresponds to 25L / h) until the feed amount reaches the target. The operating status is fed back to the MRAS control block via the OPC UA protocol. Through high-precision signal control, the system can accurately adjust the feed flow rate and feed duration, thus completing a closed-loop operation from "perception-decision-execution". The entire control process requires no manual intervention, achieving truly unmanned intelligent control.

[0052] After the replenishment is executed, the MRAS control block obtains the actual replenishment amount from the feed pump via DeltaV (e.g., the actual replenishment amount reported by the flow meter is 124.5 kg, with a deviation of 0.4% from the calculated replenishment amount of 125 kg). If the deviation is ≤5%, the replenishment is deemed qualified, and the data is recorded in RECORD_ARRAY; if the deviation is >5% (e.g., the actual replenishment amount is 118 kg, with a deviation of 5.6%), the system automatically recalculates the replenishment amount (requiring an additional 0.6 kg) and outputs a control signal until the deviation between the actual replenishment amount and the calculated value is ≤5%. At the same time, the deviation exceeding the standard is recorded in the ALARM_INFO field for subsequent traceability.

[0053] Example 5: Application flow of the predictive analytics module This embodiment uses the prediction of acid value in the production process of "resin-A" as an example to explain in detail the workflow of the predictive analysis module: S51: Data Input: The system continuously acquires data from four sampling points (time-viscosity-acid value): P1 (10:00, 70, 80.2%), P2 (10:15, 72, 79.8%), P3 (10:30, 74, 79.5%), and P4 (10:45, 76, 79.1%), and transmits the data to the predictive analysis module through the data interface module; S52: Model Construction: A time series model was constructed using linear extrapolation, with "time" as the X-axis (unit: min, 10:00 is recorded as 0 min, 10:15 is recorded as 15 min) and "acid value" as the Y-axis. The linear trend equation obtained by fitting was Y = −0.008X + 80.2 (the slope -0.008 indicates that the acid value decreases by 0.12% every 15 min). S53: Trend Prediction: Predict the acid value of the next sampling point P5 (11:00, corresponding to X=60min) as Y=-0.008×60+80.2=79.72%; S54: Warning Judgment: The lower deviation of "Resin-A" in the product database is 79.5%, and the predicted value of P5 is 79.72%, which is higher than the lower deviation. However, the system calculates that "the predicted acid value of the next 3 sampling points (up to 11:45) will drop to 79.4% (lower than the lower deviation)," thus triggering an early warning. S55: Manual intervention: The operator receives an early warning prompt (interface pop-up + audible and visual alarm), and selects to add "curing agent C" in advance (the amount to be added is calculated as 80kg). After the addition, the actual acid value of P5 is 79.6%, avoiding subsequent exceedances.

[0054] This embodiment demonstrates that the predictive analytics module can identify quality trend risks one hour in advance, providing operators with time to intervene and reducing scrap rates.

[0055] It should be noted that, for the sake of simplicity, the foregoing embodiments are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to the present invention. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to the present invention.

[0056] It should be understood that the disclosed apparatus can be implemented in other ways, as illustrated in the embodiments provided in this application. For example, the apparatus embodiments described above are merely illustrative; the division of units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or communication connections shown or discussed may be through some interfaces; the indirect coupling or communication connections between devices or units may be telecommunications or other forms.

[0057] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0058] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the scope of protection of the invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on these embodiments, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art can still combine, add, delete, or otherwise adjust the features of the various embodiments of the present invention according to the circumstances without conflict or creative effort, thereby obtaining different technical solutions that do not fundamentally depart from the concept of the present invention. These technical solutions also fall within the scope of protection of the present invention.

Claims

1. A material replenishment analysis system based on the least squares method and DeltaV system, characterized in that, include: The product library management module is used to pre-store and manage the standard parameters of different products. The standard parameters include standard curves, upper deviation curves, lower deviation curves, coordinate axis ranges, and replenishment material lists. The data interface module communicates with the DeltaV control system and the Manufacturing Execution System (MES) to acquire batch number, production line unit, product name and automatic sampling point data in real time. The curve fitting module uses the least squares method to perform polynomial curve fitting on the standard points on the standard curve, supporting fitting of up to order 9 terms, and calculates the coefficient of determination R of the fitted curve. 2 To quantify the quality of the fit; The deviation calculation module is used to compare the real-time acquired sampling point coordinates with the standard fitting curve to calculate the deviation value in the Y-axis direction. The replenishment calculation module automatically calculates the required material replenishment amount based on the deviation value, the type of replenishment material selected by the operator, and the current material weight input. The human-computer interaction module provides a graphical interface for displaying curves, deviations, and fitting quality, and for receiving parameters and instructions input manually.

2. The material replenishment analysis system based on least squares method and DeltaV system as described in claim 1, characterized in that, The curve fitting module also includes a fitting strategy switching unit, when the determination coefficient R... 2 When the deviation falls below the first preset threshold, the system allows or automatically switches the deviation calculation strategy from calculation based on the fitted curve to point-to-point calculation based on a linear function between adjacent standard points.

3. The material replenishment analysis system based on least squares method and DeltaV system as described in claim 2, characterized in that, The first preset threshold is a dynamic threshold, and its value is dynamically adjusted according to at least one of the following factors: the current production stage, the historical fitting success rate, or the stability of material batches.

4. The material replenishment analysis system based on least squares method and DeltaV system as described in claim 2 or 3, characterized in that, The fitting strategy switching unit is also configured to automatically use a local weighted regression strategy to calculate the bias when the system detects heteroscedasticity or local nonlinearity in the real-time sampling data.

5. The material replenishment analysis system based on least squares method and DeltaV system as described in claim 1, characterized in that, The supplementary amount calculation module also includes a self-learning unit, which is configured as follows: Record historical operation data, which includes at least the deviation value, the selected replenishment material, the current material weight, the calculated replenishment amount, and the evaluation of the production results after replenishment; Based on recorded historical data, the supplementation calculation model is trained or optimized through regression analysis or gradient descent to make supplementation predictions more accurate.

6. The material replenishment analysis system based on least squares method and DeltaV system as described in claim 5, characterized in that, The self-learning unit also includes a recommendation function, which is configured to recommend the most successful replenishment scheme in the historical scenario to the operator when the similarity between the current production condition and a certain scenario in the historical data exceeds a second preset threshold.

7. The material replenishment analysis system based on least squares method and DeltaV system as described in claim 1, characterized in that, It also includes a predictive analysis module, which is used to predict the Y-axis parameter value or deviation trend of the next sampling point based on the time series of data from multiple continuously acquired sampling points, and to issue an early warning when the prediction result will exceed the qualified range. The sampling period is 5-30 minutes and can be configured through the human-computer interaction module.

8. The material replenishment analysis system based on least squares method and DeltaV system as described in claim 1, characterized in that, The system is implemented as a material replenishment analysis and control block within the DeltaV system. This control block is further configured to have a control output function, which can directly output control signals to the replenishment pump or regulating valve based on the results obtained by the replenishment amount calculation module, thereby realizing closed-loop automatic control of material replenishment.

9. The material replenishment analysis system based on least squares method and DeltaV system as described in claim 1, characterized in that, The product library management module supports importing, exporting, and modifying product standard parameters via Excel files, and the system operates independently of the factory's production database.

10. A material replenishment analysis method using the system described in any one of claims 1-9, characterized in that, Includes the following steps: S1: Preset product parameters, and create or modify the product's standard curve, deviation curve, and supplementary material information through the product library management module; S2: When production starts, the batch number and product name of the current production batch are obtained from the DeltaV system through the data interface module and matched with the product database. If the match fails, an alarm is triggered. S3: After successful matching, the curve fitting module is called to fit the standard curve of the product, generate the standard fitting curve and display it in the chart of the human-computer interaction module, and at the same time display the upper and lower deviation curves. S4: Automatically receive real-time sampling point data through the data interface module or manually input data through the human-computer interaction module, and plot the data in the chart. S5: The deviation calculation module calculates the deviation value between the sampling points and the standard fitting curve, linear function, or local weighted regression line according to the current fitting strategy. S6: The operator selects to add materials based on the deviation value or system recommendation and enters the current material weight. The replenishment calculation module automatically calculates the replenishment amount. S7: Record the data from this sampling, deviation calculation, and replenishment operation to an array or database, and export it as an Excel file after the production batch is completed; S8: The system provides early warnings based on predictive analysis results, or automatically performs supplementary operations through control blocks.

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