A Smart Design Method for Drilling Fluid Formulation

Abstract

This invention discloses an intelligent drilling fluid formulation design method, comprising: collecting drilling data from various blocks; preprocessing the collected data; extracting features from the preprocessed data; training the extracted features using SVM to create a material classification model for various treatment agents in the drilling fluid formulation required for the target well; performing regression training on the drilling data from each block based on the classified drilling fluid treatment agent materials to create a regression model for the dosage of each treatment agent material; inputting new well data; and, based on the dual output requirements of classification and regression, finally obtaining the optimal drilling fluid formulation suitable for the target well; thereby improving prediction efficiency and the reliability of prediction results, and ensuring the adaptability of the drilling fluid formulation to the formation, performance, and well.

Description

Technical Field

[0001] This invention relates to the field of intelligent drilling fluid formulation design technology, and in particular to an intelligent drilling fluid formulation design method. Background Technology

[0002] Drilling in complex formations often results in numerous downhole accidents, and a good drilling fluid can effectively prevent and control these accidents. With the rapid advancement of technology in the petroleum industry, the number of drilling fluid systems has also increased. Faced with an ever-growing selection of drilling fluid systems, manual selection is becoming increasingly inefficient. Furthermore, due to the complexity and high uncertainty of oil and gas reservoir data, and the fact that the impact of certain drilling fluid systems on formation parameters cannot be precisely quantified, exhibiting a degree of fuzziness and nonlinearity, petroleum engineers typically rely on empirical formulas and other methods based on experimental analysis when precise numerical descriptions are not possible. However, this approach suffers from low prediction efficiency and large errors in the reliability of prediction results. These problems severely impact the smooth and safe operation of drilling operations. For a long time, domestic drilling companies have relied primarily on the personal experience and knowledge of experts when using drilling fluids, resulting in limited consideration of factors, low design efficiency, and a lack of data support and an intelligent drilling fluid formulation optimization design method. Summary of the Invention

[0003] The purpose of this section is to outline some aspects of embodiments of the present invention and to briefly describe some preferred embodiments. Simplifications or omissions may be made in this section, as well as in the abstract and title of this application, to avoid obscuring the purpose of these documents; however, such simplifications or omissions should not be construed as limiting the scope of the invention.

[0004] In view of the aforementioned existing problems, the present invention is proposed.

[0005] Therefore, this invention provides an intelligent design method for drilling fluid formulations to solve the problems of low prediction efficiency and large prediction error.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0007] Collect drilling data from each block, preprocess the collected data, and extract features from the preprocessed data.

[0008] Using SVM to train the extracted features, a material classification model is created for each treatment agent in the drilling fluid formulation required for the target well;

[0009] Based on the various treatment agents selected for drilling fluid, regression training was performed on drilling data from each block to create a regression model for the usage of each treatment agent.

[0010] Input new well data, and based on the dual output requirements of classification and regression, finally obtain the optimal drilling fluid formula suitable for the target well.

[0011] As a preferred embodiment of the intelligent design method for drilling fluid formulation described in this invention, the collected data undergoes preprocessing, which includes data cleaning and standardization, comprising the following steps:

[0012] Detection and processing of duplicate values: For duplicate data in well information and formation information, direct deletion is adopted; for characteristic duplicate data, the corr function is used to detect similarity, and the correlation coefficients of linear data, unordered sequences and nonlinear data are calculated by using three correlation analysis methods: Pearson, Kendall and Spearman. A similarity of 1 means that the data are the same, so one of them is deleted.

[0013] Detection and handling of missing values: By checking for missing and non-missing values ​​in well and formation information, missing values ​​are predicted based on other non-missing variables using the interpolate module provided by SciPy.

[0014] Detection and handling of outliers: Use the 3δ principle to detect values ​​that deviate significantly, and delete outliers directly;

[0015] Data standardization processing: The standard deviation standardization method is used, i.e., new data = (original data - original mean) / original standard deviation. The numerical data in well information and formation information after standardization are normally distributed with a mean of 0 and a variance of 1.

[0016] Data transformation: For non-numerical data such as formation lithology, drilling fluid performance indicators, and drilling fluid materials, the get_dummies function provided by the Pandas library is used to obtain and transform the non-numerical data into numerical data.

[0017] In a preferred embodiment of the intelligent drilling fluid formulation design method described in this invention, during the feature extraction of the preprocessed data, all features of well information, formation information, and performance indicators are centered, i.e., the mean is removed, and the average value of each feature is calculated. Represented as:

[0018]

[0019] in, Let M be the average value for each feature, and M be the number of samples for a particular feature. For a certain feature X a The i-th sample below.

[0020] As a preferred embodiment of the intelligent design method for drilling fluid formulation described in this invention, in the feature extraction of the preprocessed data, a covariance greater than 0 indicates that two features increase or decrease together; a covariance less than 0 indicates that one increases and the other decreases; when equal to 0, the two features are independent, and the larger the absolute value of the covariance, the greater the influence of the two features on each other, and vice versa; the covariance matrix C of all features of well information, formation information, and performance indicators is represented as:

[0021]

[0022] in, For feature X a and X b The covariances of a and b are (1, 2, 3, ..., n).

[0023] As a preferred embodiment of the intelligent design method for drilling fluid formulation described in this invention, in the feature extraction of the preprocessed data, the eigenvalues ​​λ and corresponding eigenvectors u of the covariance matrix C are calculated. There will be n eigenvalues ​​λ, and each λ... i Corresponding to a feature vector u i Sort the eigenvalues ​​λ in descending order, select the k largest eigenvalues, and extract the corresponding k eigenvectors to obtain a set {(λ1, u1), (λ2, u2), (λ3, u3), ..., (λ...}. k u k The value of k is selected based on whether the cumulative variance contribution rate Q is greater than 85%; the cumulative variance contribution rate Q is expressed as:

[0024]

[0025] As a preferred embodiment of the intelligent drilling fluid formulation design method of the present invention, wherein: in the feature extraction of the preprocessed data, the original features are projected onto the selected feature vector to obtain a new k-dimensional feature after dimensionality reduction; for any sample X among well information, formation information, and performance indicators... i The original characteristics are The new features after projection are Thus, dimensionality reduction is achieved, and the formula for calculating the new features is as follows:

[0026]

[0027] As a preferred embodiment of the intelligent drilling fluid formulation design method of the present invention, the step of creating a material classification model for each treatment agent in the drilling fluid formulation required for the target well includes the following steps:

[0028] Using the feature vectors from well information, formation information, and performance indicators as input data, and labeling the drilling fluid materials contained in a certain type of treatment agent as 1, 2, 3, ... as output data, a dataset is established.

[0029] The dataset was divided into a training set and a test set for the model in a 7:3 ratio.

[0030] Multiple weak classifiers were obtained by using the SVM algorithm for multiple rounds of training.

[0031] A strong classifier is obtained by weighted summation of multiple weak classifiers. Well information, formation information, and performance indicators are input into the strong classifier, which outputs the required materials for various treatment agents in the drilling fluid formulation.

[0032] As a preferred embodiment of the intelligent design method for drilling fluid formulation described in this invention, in the process of classifying the treatment agent material and obtaining multiple weak classifiers, the method specifically involves training the first weak classifier starting from the training sample set A, calculating the weak classifier coefficients based on the error rate, updating the weights of the data, using the new weights to train and obtain the second weak classifier, and so on to obtain multiple weak classifiers.

[0033] As a preferred embodiment of the intelligent design method for drilling fluid formulation described in this invention, the step of obtaining weak classifiers involves weighting and summing all the weak classifiers according to their respective weight coefficients to obtain a strong classifier.

[0034] As a preferred embodiment of the intelligent design method for drilling fluid formulation described in this invention, the step of creating a regression model for the dosage of various treatment agent materials includes the following steps:

[0035] The feature vectors in well information, formation information and performance indicators are set as independent variables x1, x2, ..., xn, and the amount of a certain treatment agent material is set as y;

[0036] Establish a multiple linear regression model: Y = β0 + β1x1 + β2x2 + ... + β n x n +ε;

[0037] Input the observed values ​​of the independent and dependent variables, and calculate the parameter β in the regression model. n ε;

[0038] Perform significance tests on the independent variables to determine whether each independent variable has a significant effect on the dependent variable;

[0039] The goodness of fit of the regression model, i.e., R0 2 The closer the value is to 1, the better the regression fit; conversely, the smaller the value is, the worse the fit.

[0040] The beneficial effects of this invention are as follows: This invention employs an intelligent drilling fluid formulation design method, which preprocesses and extracts features from multi-source information including well information, formation information, performance indicators, and drilling fluid formulation. Secondly, it uses SVM to train the features, establishing a material classification model for each treatment agent in the drilling fluid formulation required for the target well. Finally, through regression training, it establishes a regression model for the dosage of each treatment agent material, thereby improving prediction efficiency and the reliability of prediction results, and ensuring the adaptability of the drilling fluid formulation to different formations, performance characteristics, and well conditions. Attached Figure Description

[0041] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. Wherein:

[0042] Figure 1 This is a basic flowchart illustrating a drilling fluid formulation intelligent design method according to an embodiment of the present invention.

[0043] Figure 2 A basic model diagram of a drilling fluid formulation intelligent design method provided in one embodiment of the present invention;

[0044] Figure 3 A comparison chart of the prediction accuracy of three models for an intelligent drilling fluid formulation design method provided in one embodiment of the present invention;

[0045] Figure 4 A comparison chart of processing times for three models of an intelligent drilling fluid formulation design method provided in one embodiment of the present invention;

[0046] Figure 5 A comparison chart of RMSE values ​​for three models of an intelligent drilling fluid formulation design method provided in one embodiment of the present invention. Detailed Implementation

[0047] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0048] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0049] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0050] This invention is described in detail with reference to the schematic diagrams. When detailing the embodiments of this invention, for ease of explanation, the cross-sectional views illustrating the device structure may be partially enlarged, not adhering to the usual scale. Furthermore, the schematic diagrams are merely examples and should not be construed as limiting the scope of protection of this invention. In actual fabrication, the three-dimensional spatial dimensions of length, width, and depth should be included.

[0051] Furthermore, in the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are used solely for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. In addition, the terms "first," "second," or "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0052] Unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" in this invention should be interpreted broadly. For example, they can refer to fixed connections, detachable connections, or integral connections; similarly, they can refer to mechanical connections, electrical connections, or direct connections, or indirect connections through an intermediate medium, or internal connections between two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0053] Example 1

[0054] Reference Figure 1-2 As one embodiment of the present invention, a method for intelligent design of drilling fluid formulations is provided, such as... Figure 1 As shown, it includes the following steps:

[0055] S1: Collect drilling data from each block, preprocess the collected data, and extract features from the preprocessed data.

[0056] Furthermore, the collected data undergoes preprocessing, which includes data cleaning and standardization, comprising the following steps:

[0057] A1: Detection and handling of duplicate values: For duplicate data in well information and formation information, direct deletion is adopted; for characteristic duplicate data, the corr function is used to detect similarity, and the correlation coefficients of linear data, unordered sequences and nonlinear data are calculated by using three correlation analysis methods: Pearson, Kendall and Spearman. A similarity of 1 means that the data are the same, so one of them is deleted.

[0058] A2: Detection and handling of missing values: By checking for missing and non-missing values ​​in well and formation information using isnull and notnull, missing values ​​can be predicted based on other non-missing variables using the interpolate module provided by Scipy.

[0059] A3: Detection and handling of outliers: Use the 3δ principle to detect values ​​that deviate significantly, and delete outliers directly;

[0060] A4: Data standardization: The standard deviation standardization method is used, i.e., new data = (original data - original mean) / original standard deviation. The standardized data of numerical data in well information and formation information follows a normal distribution with a mean of 0 and a variance of 1.

[0061] A5: Data Conversion: For non-numerical data such as formation lithology, drilling fluid performance indicators, and drilling fluid materials, use the get_dummies function provided by the Pandas library to obtain and convert the non-numerical data into numerical data.

[0062] Furthermore, feature extraction is performed on the preprocessed data, including the following steps: B1: Centering, i.e., removing the mean, is performed on all features of well information (such as well depth, inclination angle, azimuth, etc.), formation information (lithology, temperature, pressure, porosity, fracture width, etc.) and performance indicators (temperature resistance, salt resistance, pressure bearing capacity, etc.). The average value of each feature is calculated using the following formula. Then for all samples, for each feature X a Subtract its own mean from each average value Represented as:

[0063] a is (1, 2, 3, ..., n)

[0064] in, Let M be the average value for each feature, and M be the number of samples for a particular feature. For a certain feature X a The i-th sample below.

[0065] B2: Calculate the covariance matrix C of all features including well information (such as well depth, inclination angle, azimuth, etc.), formation information (lithology, temperature, pressure, porosity, fracture width, etc.), and performance indicators (temperature resistance, salt resistance, pressure bearing capacity, etc.). A covariance greater than 0 indicates that both features increase or decrease together; less than 0 indicates that one increases while the other decreases; and equal to 0 indicates that they are independent. The larger the absolute value of the covariance, the greater the influence of each feature on the other, and vice versa. The covariance matrix C is expressed as:

[0066]

[0067] in, For feature X a and X b The covariances of a and b are (1, 2, 3, ..., n).

[0068] B3: Find the eigenvalues ​​λ and corresponding eigenvectors u of the covariance matrix C. There will be n eigenvalues ​​λ, each λ... i Corresponding to a feature vector u i Sort the eigenvalues ​​λ in descending order, select the k largest eigenvalues, and extract their corresponding k eigenvectors to obtain a set {(λ1, u1), (λ2, u2), (λ3, u3), ..., (λ...}. k u k The value of k is selected based on whether its cumulative variance contribution rate Q is greater than 85%; the cumulative variance contribution rate Q is expressed as:

[0069]

[0070] B4: Project the original features onto the selected feature vector to obtain the new k-dimensional features after dimensionality reduction. For any sample X from well information, formation information, and performance indicators... i The original characteristics are The new features after projection are Thus, dimensionality reduction is achieved, and the formula for calculating the new features is as follows:

[0071]

[0072] S2: Use SVM to train the extracted features and create a material classification model for each treatment agent in the drilling fluid formulation required for the target well;

[0073] Furthermore, a material classification model is created for the various treatment agents in the drilling fluid formulation required for the target well, such as... Figure 2 As shown, it includes the following steps:

[0074] C1: Using the feature vectors from well information, formation information, and performance indicators as input data, and labeling the drilling fluid materials contained in a certain type of treatment agent in Table 1 as 1, 2, 3, ... as output data, a dataset is established.

[0075] C2: Divide the dataset into the training set and the test set of the model in a 7:3 ratio.

[0076] C3: Use the SVM algorithm for multiple rounds of training to obtain multiple weak classifiers.

[0077] C4: A strong classifier is obtained by weighted summation of multiple weak classifiers. Well information, formation information and performance indicators are input into the strong classifier, and the required materials for various treatment agents in the drilling fluid formulation are output.

[0078] Table 1. Drilling Fluid Material Label Numbering Table

[0079]

[0080]

[0081] S3: Based on the selected drilling fluid treatment materials, regression training is performed on the drilling data of each block to create a regression model for the usage of each treatment material;

[0082] Furthermore, a regression model was created regarding the dosage of each treatment agent material, including the following steps:

[0083] D1: Set the feature vectors in the well information, formation information and performance indicators as independent variables x1, x2, ..., xn, and set the amount of a certain treatment agent material in Table 1 as y.

[0084] D2: Establish a multiple linear regression model: Y = β0 + β1x1 + β2x2 + ... + β n x n +ε;

[0085] D3: Input the observed values ​​of the independent and dependent variables, and calculate the parameter β in the regression model. n ε;

[0086] D4: Perform a significance test on the independent variables to determine whether each independent variable has a significant effect on the dependent variable;

[0087] D5: The goodness of fit of the regression model, i.e., R0 2 The closer the value is to 1, the better the regression fit; conversely, the smaller the value is, the worse the fit.

[0088] S4: Input new well data, and based on the dual output requirements of classification and regression, finally obtain the optimal drilling fluid formula suitable for the target well.

[0089] It should be noted that since drilling fluid formulation design involves classification and regression problems of high-dimensional features and has a limited sample size, support vector machine (SVM) is more suitable for intelligent design of drilling fluid formulation. It can find the best result between the learning accuracy and learning ability of well information, formation information and performance indicators, so that the generalization ability reaches the optimal level. Therefore, this indicator is the decisive indicator.

[0090] Example 2

[0091] Reference Figure 3-5 As an embodiment of the present invention, a method for intelligent design of drilling fluid formulation is provided. To verify its beneficial effects, a comparison of multiple schemes is provided.

[0092] Figures 3-5 The performance comparison of three models for intelligent design of drilling fluid formulations is presented. Figure 3 This shows a comparison of the prediction accuracy of the three models. The accuracy is the main criterion for selecting the best model. SVM has the highest accuracy at 94%, followed by neural network at 91%, and decision tree has the lowest accuracy at 88%. Figure 4 The comparison shows the processing time of the three models: the neural network takes 12.56 seconds, the decision tree takes 20.23 seconds, and the SVM takes only 3.67 seconds. A shorter processing time indicates that the model is better suited to handling the target problem and has a faster processing speed and response. Figure 5 The chart compares the RMSE values ​​of the three models. When dealing with regression problems involving drilling fluid formulation dosages, a smaller RMSE value indicates lower dispersion and smaller error. The comparison chart shows that SVM is more suitable for predicting drilling fluid formulations, improving prediction efficiency and reliability, and ensuring the adaptability of drilling fluid formulations to different formations, performance characteristics, and well conditions.

[0093] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for intelligent design of drilling fluid formulations, characterized in that, include: Drilling data from each block is collected, the collected data is preprocessed, and features are extracted from the preprocessed data. The drilling data includes well information, formation information, drilling fluid performance indicators, and drilling fluid materials. Using SVM to train the extracted features, a material classification model for various treatment agents in the drilling fluid formulation required for the target well is created; Based on the various treatment agents selected for drilling fluid, regression training was performed on drilling data from each block to create a regression model for the usage of various treatment agents. Input new well data, and based on the dual output requirements of classification and regression, finally obtain the optimal drilling fluid formula suitable for the target well; In feature extraction of the preprocessed data, the eigenvalues ​​λ and corresponding eigenvectors u of the covariance matrix C are calculated. There will be n eigenvalues ​​λ, each λ... i Corresponding to a feature vector u i Sort the eigenvalues ​​λ in descending order, select the k largest eigenvalues, and extract the corresponding k eigenvectors to obtain a set {(λ1, u1), (λ2, u2), (λ3, u3), ..., (λ... k u k The value of k is selected based on whether the cumulative variance contribution rate Q is greater than 85%; the cumulative variance contribution rate Q is expressed as: The creation of a material classification model for various treatment agents in the drilling fluid formulation required for the target well includes the following steps: Using the feature vectors from well information, formation information, and performance indicators as input data, and labeling the drilling fluid materials contained in a certain type of treatment agent as 1, 2, 3, ... as output data, a dataset is established. The dataset was divided into a training set and a test set for the model in a 7:3 ratio. Multiple weak classifiers were obtained by using the SVM algorithm for multiple rounds of training. A strong classifier is obtained by weighted summation of multiple weak classifiers. Well information, formation information and performance indicators are input into the strong classifier, and the required materials for various treatment agents in the drilling fluid formulation are output. In the classification of treatment agent materials, multiple weak classifiers are obtained through multiple rounds of training. Specifically, the first weak classifier is trained starting from the training sample set A. The coefficients of the weak classifier are calculated based on the error rate, the weights of the data are updated, and the second weak classifier is obtained by training with the new weights. This process is repeated to obtain multiple weak classifiers. To obtain a strong classifier, we need to sum all the weak classifiers according to their respective weight coefficients.

2. The intelligent design method for drilling fluid formulation as described in claim 1, characterized in that: The collected data undergoes preprocessing, which includes data cleaning and standardization, comprising the following steps: Detection and processing of duplicate values: For duplicate data in well information and formation information, direct deletion is adopted; for characteristic duplicate data, the corr function is used to detect similarity, and the correlation coefficients of linear data, unordered sequences and nonlinear data are calculated by using three correlation analysis methods: Pearson, Kendall and Spearman. A similarity of 1 means that the data are the same, so one of them is deleted. Detection and handling of missing values: By checking for missing and non-missing values ​​in well and formation information, missing values ​​are predicted based on other non-missing variables using the interpolate module provided by SciPy. Detection and handling of outliers: Use the 3δ principle to detect values ​​that deviate significantly, and delete outliers directly; Data standardization processing: The standard deviation standardization method is used, that is, new data = (original data - original mean) / original standard deviation. The numerical data in well information and formation information after standardization are normally distributed with a mean of 0 and a variance of 1. Data transformation: Non-numerical data on formation lithology, drilling fluid performance indicators, and drilling fluid materials are obtained using the get_dummies function provided by the Pandas library and transformed into numerical data.

3. The intelligent design method for drilling fluid formulation as described in claim 1 or 2, characterized in that: In the feature extraction process for the preprocessed data, all features of well information, formation information, and performance indicators are centered, i.e., mean-removed, and the average value of each feature is calculated. Represented as: in, Let M be the average value for each feature, and M be the number of samples for a particular feature. For a certain feature The i-th sample below.

4. The intelligent design method for drilling fluid formulation as described in claim 3, characterized in that: In the feature extraction of the preprocessed data, a covariance greater than 0 indicates that two features are increasing or decreasing together; less than 0 indicates that one is increasing and the other is decreasing; when equal to 0, the two features are independent. The larger the absolute value of the covariance, the greater the influence of each feature on the other, and vice versa. The covariance matrix C of all features of well information, formation information, and performance indicators is expressed as: in, Features and The covariances, a, b for .

5. The intelligent design method for drilling fluid formulation as described in claim 4, characterized in that: In the feature extraction process for the preprocessed data, the original features are projected onto the selected feature vector to obtain a new k-dimensional feature after dimensionality reduction; for any sample X among well information, formation information, and performance indicators... i The original characteristics are ( , , ..., ,) T The new features after projection are ( , , ..., ,) T Thus, dimensionality reduction is achieved, and the formula for calculating the new features is as follows: 。 6. The intelligent design method for drilling fluid formulation as described in claim 5, characterized in that: The creation of a regression model for the dosage of various treatment agents includes the following steps: The feature vectors obtained from well information, formation information, and performance indicators after dimensionality reduction are set as independent variables. y is the amount of a certain treatment agent material used. Establish a multiple linear regression model: ; Input the observed values ​​of the independent and dependent variables, and calculate the parameters in the regression model. , ; Perform significance tests on the independent variables to determine whether each independent variable has a significant effect on the dependent variable; The goodness of fit of the regression model, i.e., R0 2 The closer the value is to 1, the better the regression fit; conversely, the smaller the value is, the worse the fit.

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