Method for monitoring based on data dependent kernel canonical variate analysis with joint sparsity constraints

Abstract

The application discloses a kind of based on joint sparse constraint data dependent kernel canonical variable analysis monitoring method, in combination isolated kernel and principal component analysis dependent blast furnace data nonlinear feature extraction framework is proposed, obtain the data dependent nonlinear feature with discriminant ability is used to detect fault;After extracting nonlinear feature, using I 2,0 Norm joint sparse constraint canonical variable analysis method further explores the dynamics of blast furnace ironmaking process;By combining manifold-constrained gradient descent method and gradient hard threshold tracking method, an efficient two-stage iterative alternating direction multiplier method is designed to solve the new optimization objective;Then, T 2 Statistics and its corresponding control limit real-time monitoring blast furnace ironmaking process.The application proposes a kind of dependent nonlinear feature extraction framework based on IK, which has wide applicability;Eliminate the influence of redundant or even negative nonlinear relationship and outliers;Improve the robustness and accuracy of canonical variable space.

Description

Technical Field

[0001] This invention relates to the field of monitoring blast furnace ironmaking processes, and in particular to a monitoring method based on data-dependent kernel canonical variable analysis with joint sparse constraints. Background Technology

[0002] As a core component of steel production, the stable operation of the blast furnace is crucial for ensuring efficient steel production. However, various abnormal situations may occur during blast furnace ironmaking, negatively impacting production. These abnormalities lead to decreased iron output, affecting production efficiency and economic benefits. Furthermore, they may increase energy consumption, resulting in resource waste and a heavier environmental burden. More seriously, abnormalities can cause equipment damage or even trigger major safety accidents, threatening personnel safety and stable equipment operation. Therefore, effective real-time monitoring of the blast furnace ironmaking process is essential to promptly detect abnormalities and take appropriate measures for adjustment and optimization.

[0003] Blast furnace ironmaking is a metallurgical process that transforms iron ore into molten iron. This process is a continuous production method, where raw materials interact from top to bottom while gases move in the opposite direction from bottom to top. Blast furnace ironmaking involves the proportional mixing and grinding of solid raw materials such as iron ore, limestone, and coke. These materials are then fed into the upper part of the blast furnace. Preheated air and pulverized coal are injected into the blast furnace, where combustion produces high-temperature, high-pressure reducing gases. As these gases rise, they heat the furnace charge, leading to a series of complex physical and chemical transformations. These reactions reduce iron oxide in the iron ore to molten iron, which can be collected through the taphole. Additionally, limestone and other substances are injected into the blast furnace hearth to react with impurities in the charge, promoting slag separation. Since blast furnace exhaust gases and flue gases contain a large amount of heat energy, they are typically collected for power generation or to heat the furnace charge. Given the complexity of the blast furnace ironmaking process, its dynamic nature, complex nonlinearity, numerous variables, noise, and the presence of outliers pose significant challenges to process monitoring.

[0004] The survey results show that fault identification in blast furnace ironmaking currently relies mainly on the experience of operators. However, this method has two significant drawbacks. First, accumulating fault identification experience takes several years, which is a challenge for new personnel and limits the speed and accuracy of fault identification. Second, continuously observing data curves is a tedious task, easily leading to operator fatigue and errors. However, with the continuous improvement of industrial informatization, data-driven process monitoring has become a key technology for improving industrial safety, quality, and operational efficiency. In large blast furnaces, data exhibits nonlinear and time-varying characteristics, making anomaly monitoring and diagnosis a cutting-edge research hotspot and challenge in metallurgical technology. Therefore, to overcome the limitations of traditional fault identification methods, increasing research focuses on data-based monitoring and diagnostic technologies. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, the present invention aims to provide a Joint Sparse Constraint Data Dependency Kernel Canonical Variable Analysis (JS-DDKCVA) method to improve the monitoring performance of the blast furnace ironmaking process.

[0006] The technical solution for achieving the technical objective of this invention is as follows:

[0007] A monitoring method based on Joint Sparse Constraint Data Dependency Kernel Canonical Variable Analysis (JS-DDKCVA) is proposed. Combining Isolated Kernel (IK) and Principal Component Analysis (PCA), a nonlinear feature extraction framework dependent on blast furnace data is constructed to obtain discriminative data-dependent nonlinear features for fault detection. After extracting the nonlinear features, l is used... 2，0 The canonical variable analysis (CVA) method with norm joint sparse constraints is used to further explore the dynamics of the blast furnace ironmaking process. An efficient two-stage iterative alternating direction multiplier method (TPI-ADMM) is designed by combining the manifold-constrained gradient descent (MCGD) method and the gradient hard threshold pursuit (GHTP) method to solve the new optimization objective. Then, T... 2 Statistical parameters and their corresponding control limits are used to monitor the blast furnace ironmaking process in real time.

[0008] The nonlinear feature extraction framework that relies on blast furnace data is as follows:

[0009] IK is derived directly from the data by adapting to the local data density structure, and is used to enhance the ability to distinguish between normal and faulty blast furnace samples, as follows:

[0010] Let DS = {u(1), u(2), ..., u(σ)} be the blast furnace sample dataset; first, randomly sample ρ points from the data sample, and use the Venn diagram method to partition the data space based on each sample point; let P ρ(DS) represents the set of all available partitions P in the dataset DS, where each partition ψ∈P will be a random subset. One data point is isolated from the rest of the data points; IK is calculated as the expectation that any two points u(i) and u(j)∈DS fall into the same isolation partition ψ∈P;

[0011] K = <Φ(u(i)), Φ(u(j))> F =E P (DS)[I(u(i),u(j)∈ψ|ψ∈P)]

[0012] Where, I(·) = 1 when the condition within the parentheses is met; based on the Monte Carlo method, the operation of partitioning the data space is repeated independently t times; IK is represented as:

[0013]

[0014] Where i, j = 1, 2, ... σ; then, the average central kernel matrix is ​​calculated using the following formula.

[0015]

[0016] Where matrix C σ ∈R σ×σ All elements are composed of Composition; In order to extract the main features in the F space, the following eigenvalue decomposition is performed:

[0017]

[0018] where Λ=[λ1, λ2,...,λ σ ] T and Γ=[γ1,γ2,...,γ σ ] T Let represent the eigenvalue matrix and eigenvector matrix, respectively; then, the nonlinear eigenma matrix Z, containing the main information, is given by n (n < σ) largest eigenvalues ​​and their corresponding orthogonal eigenvectors.

[0019]

[0020] The method described above integrates the obtained nonlinear features into l 2，0 The new optimization objective proposed in the canonical variable analysis (CVA) of norm joint sparse constraints is:

[0021] First, JS-DDKCVA transforms the data-dependent nonlinear feature matrix Z∈R σ×n Divided into past Hankel matrix Z p ∈R m×ns And the future Hankel matrix Z f∈R m×ns The goal of the model is to find a pair of joint sparse canonical matrices J and L such that Z p J and Z f To maximize the correlation between L, the model is constructed as follows:

[0022]

[0023] stJ T Z p T Z p J = 1, L T Z f T Z f L=1

[0024] Where λ1 and λ2 represent regularization parameters, r is the number of regularization variables, and ||·|| 2，0 Represent l 2，0 Norm, l 2，0 The norm is a combination of the l0 norm and the l2 norm, calculated as follows:

[0025] ||A|| 2，0 =#{i:||a i ||2≠0}

[0026] Where #{·} represents the cardinality.

[0027] The efficient two-stage iterative alternating direction multiplier method (TPI-ADMM) designed by combining the manifold-constrained gradient descent (MCGD) method and the gradient hard threshold pursuit (GHTP) method is as follows:

[0028] If L is fixed, then the following optimization problem is obtained:

[0029]

[0030] stJ T Z p T Z p J = 1;

[0031] When J is fixed, the optimization problem for solving L is:

[0032]

[0033] stL T Z f T Z f L = 1;

[0034] The solution to J and L is obtained by alternating iterations in two stages until J and L converge.

[0035] To solve for J, we introduce the auxiliary variable A = Z. p J and make Z f L = E, the optimization problem can be written in the following augmented Lagrangian form:

[0036]

[0037] Where W represents the Lagrange multiplier, β > 0 represents the penalty parameter, and A needs to satisfy the constraint M{A|A T A = Ir}, solve using the Alternating Direction Multiplier Method (ADMM) in the order of optimization of A, J, W;

[0038] To solve subproblem A, the optimization problem simplifies to the following form:

[0039]

[0040] stA T A = 1;

[0041] When A and W are fixed, the J subproblem becomes:

[0042]

[0043] set up Next, the GHTP algorithm can be used to solve for L;

[0044] After J and L are determined, W is calculated using the following formula:

[0045] W k+1 =W k -β(A k+1 -Z p J k+1 );

[0046] Following the above operations, the dynamic projection matrix J with joint sparse constraints is obtained. Then, the data-related blast furnace nonlinear eigenvectors are transformed into q-dimensional regularized variables. This variable is believed to contain essential information that helps in monitoring the blast furnace ironmaking process.

[0047] =Z p J∈R m×r .

[0048] The method described herein has the following process:

[0049] Step 1: Offline modeling;

[0050] Step 1.1: In the fault detection method based on JS-DDKCVA, T is used. 2As a monitoring statistic, the statistic is given by the following formula:

[0051]

[0052] in, and represent time k The i-th element;

[0053] Step 1.2: Calculate T 2 To estimate the control limits of the statistic, due to the non-Gaussian distribution of the state variables and residuals, the kernel density estimation (KDE) method is chosen.

[0054] Step Two: Real-time Monitoring;

[0055] First, real-time data is collected and standardized. Then, a real-time statistic T is constructed using a pre-trained JS-DDKCVA model. 2 The process operating status is determined by comparing whether the statistical value is less than the control limit; if T 2 If the value exceeds the control limit, the process is considered to be in an abnormal state; otherwise, the process is considered to be normal and requires no maintenance.

[0056] The beneficial effects of this invention are as follows:

[0057] 1. Combining isolated nuclei (IK), l 2，0 Leveraging the advantages of norm-based sparse constraints and canonical variable analysis (CVA), an innovative process monitoring method is proposed to address the nonlinear and dynamic characteristics of blast furnace ironmaking processes.

[0058] 2. A data-dependent nonlinear feature extraction framework based on IK is proposed. This framework has broad applicability and facilitates fault identification. IK can adapt to data density distribution and can obtain more sensitive data-related nonlinear features.

[0059] 3. Joint sparsity constraint 2，0 The norm is introduced into CVA, thus developing a novel optimization objective. By imposing this constraint, redundant or side-effect-laden nonlinear information can be filtered out, and the influence of outliers can be eliminated. This approach improves robustness and accuracy in the canonical variable space.

[0060] 4. A two-stage iterative alternating direction multiplier descent (TPI-ADMM) method is designed, which combines the manifold-constrained gradient descent (MCGD) method and the gradient hard threshold pursuit (GHTP) method. This algorithm can effectively optimize the proposed JS-DDKCVA method. Attached Figure Description

[0061] Figure 1The diagram shows an offline modeling and online monitoring method for monitoring the blast furnace ironmaking process based on Joint Sparse Constraint Data Dependency Kernel Canonical Variable Analysis (JS-DDKCVA) according to the present invention.

[0062] Figure 2 This is the monitoring result of JS-DDKCVA on suspended material failure.

[0063] Figure 3 The results of JS-DDKCVA monitoring of pipeline faults. Detailed Implementation

[0064] To more clearly describe the technical solution of the present invention, the following description is provided in conjunction with the accompanying drawings and embodiments.

[0065] like Figure 1 The diagram shown is a schematic representation of the monitoring method based on joint sparse constraints and kernel canonical variable analysis of data dependence according to the present invention.

[0066] A blast furnace ironmaking process monitoring method based on Joint Sparse Constraint Data Dependency Kernel Canonical Variable Analysis (JS-DDKCVA) is proposed. This invention combines Isolated Kernel (IK) and Principal Component Analysis (PCA) to propose a nonlinear feature extraction framework dependent on blast furnace data, obtaining data-dependent nonlinear features with strong discriminative capabilities for fault detection. After extracting the nonlinear features, l is used... 2，0 The canonical variable analysis (CVA) method with norm-joint sparse constraints further explored the dynamics of the blast furnace ironmaking process. An efficient two-stage iterative alternating direction multiplier method (TPI-ADMM) was designed by combining the manifold-constrained gradient descent (MCGD) method and the gradient hard threshold pursuit (GHTP) method to solve the new optimization objective. Then, T... 2 Statistical parameters and their corresponding control limits are used to monitor the blast furnace ironmaking process in real time.

[0067] The nonlinear feature extraction framework that relies on blast furnace data is as follows:

[0068] Kernel methods have been widely used to explore the nonlinear characteristics of blast furnace ironmaking processes. They can project nonlinear input data into a higher-dimensional feature space F, facilitating the application of linear methods in this transformed space. Isolated kernels (IK) can address the mediocre performance of traditional kernel methods in specific tasks such as process monitoring. IK can be derived directly from the data by adapting to the local data density structure, thus enhancing the ability to distinguish between normal and faulty blast furnace samples. Its form is as follows:

[0069] Let DS = {u(1), u(2), ..., u(σ)} be the blast furnace sample dataset. First, ρ random samples are drawn from the data sample, and the data space is partitioned using the Venn diagram method with each sample point as the basis. Let P... ρ (DS) represents the set of all available partitions P in the dataset DS, where each partition ψ∈P will be a random subset. One data point is isolated from the rest of the data points. IK can be calculated as the expectation that any two points u(i), u(j)∈DS fall into the same isolation partition ψ∈P.

[0070] K = <Φ(u(i)), Φ(u(j))> F =E P (DS)[I(u(i),u(j)∈ψ|ψ∈P)]

[0071] Wherein, I(·) = 1 when the condition within the parentheses is satisfied. In practical applications, based on the Monte Carlo method, the operation of partitioning the data space can be repeated independently t times. In this way, IK is represented as:

[0072]

[0073] Where i, j = 1, 2, ... σ. Then, the average central kernel matrix is ​​calculated using the following formula.

[0074]

[0075] Where matrix C σ ∈R σ×σ All elements are composed of Composition. To extract the main features in the F space, the following eigenvalue decomposition is performed:

[0076]

[0077] where Λ=[λ1, λ2,...,λ σ ] T and Γ=[γ1,γ2,...,γ σ ] T Let represent the eigenvalue matrix and the eigenvector matrix, respectively. Then, the nonlinear eigenma matrix Z, which contains the main information, can be given by n (n < σ) largest eigenvalues ​​and their corresponding orthogonal eigenvectors.

[0078]

[0079] The obtained nonlinear features are integrated into l 2，0 The new optimization objective proposed in the canonical variable analysis (CVA) of norm joint sparse constraints is:

[0080] To obtain joint sparse dynamic nonlinear information during the blast furnace ironmaking process, JS-DDKCVA employs l 2，0 Norms effectively filter out redundant or even negative nonlinear information, mitigating the impact of outliers.

[0081] First, JS-DDKCVA transforms the data-dependent nonlinear feature matrix Z∈R σ×n Divided into past Hankel matrix Z p ∈R m×ns And the future Hankel matrix Z f ∈R m×ns The goal of the model is to find a pair of joint sparse canonical matrices J and L such that Z p J and Z f The correlation between L is maximized. The model is constructed as follows:

[0082]

[0083] stJ T Z p T Z p J = 1, L T Z f T Z f L=1

[0084] Where λ1 and λ2 represent regularization parameters, r is the number of regularization variables, and ||·|| 2，0 Represent l 2，0 Norm. 2，0 The norm is a combination of the l0 norm and the l2 norm, calculated as follows:

[0085] ||A|| 2，0 =#{i:||a i ||2≠0}

[0086] Where #{·} represents the cardinality.

[0087] The efficient two-stage iterative alternating direction multiplier method (TPI-ADMM) designed by combining the manifold-constrained gradient descent (MCGD) method and the gradient hard threshold pursuit (GHTP) method is as follows:

[0088] Because of l 2，0 The norm constraint is non-convex, thus the optimization problem may be more difficult. Referring to the Gauss-Seidel approach, when other variables are fixed, the parameters can be updated by minimizing the objective function. If L is fixed, the following optimization problem can be obtained:

[0089]

[0090] stJ T Z p T Z p J = 1

[0091] Similarly, when J is fixed, an optimization problem for solving L can be obtained. The problem is:

[0092]

[0093] stL T Z f T Z f L=1

[0094] Therefore, J and L can be solved iteratively in two stages until they converge. After introducing the overall iterative algorithm, the following demonstrates an optimization algorithm based on TPI-ADMM for solving the J problem, which is the same as for solving L. Taking the solution of J as an example, an auxiliary variable A = Z is introduced. p J and make Z f L = E, so the optimization problem can be written in the form of an augmented Lagrangian function as follows.

[0095]

[0096] Where W represents the Lagrange multiplier, and β > 0 represents the penalty parameter. A is required to satisfy the constraint M{A|A T A = Ir}. To address this problem, the Alternating Direction Multiplier Method (ADMM) is applied, with optimization in the order of A, J, W.

[0097] To solve subproblem A, the optimization problem can be simplified to the following form:

[0098]

[0099] stA T A = 1

[0100] It can be noted that, due to its Stiefel manifold constraint M{A|A T The problem is nonconvex, where A = Ir. Manifold optimization is a recently proposed method for solving and analyzing manifold-constrained optimization problems. A contraction function R based on extreme decomposition is chosen. X (G)=(X+G)(I+G T G) -12 Then, the manifold constrained gradient descent (MCGD) method is used to obtain the solution to subproblem A.

[0101] When A and W are fixed, the J subproblem becomes:

[0102]

[0103] Because there is l 2，0 The norm, calculating the value of J, is NP-hard. Iterative hard thresholding (IHT) methods are significant in solving nonconvex optimization problems based on the l0 norm and offer many improvements. In this invention, an iterative greedy selection algorithm called Gradient Hard Thresholding Pursuit (GHTP) is applied to solve the problem. Let... Next, the GHTP algorithm can be used to solve for L.

[0104] Once J and L are determined, W can be calculated using the following formula:

[0105] W k+1 =W k -β(A k+1 -Z p J k+1 )

[0106] The above describes the specific methods for each sub-step of the TPI-ADMM algorithm. After the above operations, the dynamic projection matrix J of the joint sparse constraints is obtained. Then, the data-related nonlinear eigenvectors of the blast furnace can be converted into q-dimensional regularized variables. This variable is believed to contain essential information that helps monitor the blast furnace ironmaking process.

[0107]

[0108] like Figure 1 As shown, one specific process is as follows:

[0109] Step 1: Offline modeling;

[0110] Step 1.1: In the fault detection method based on JS-DDKCVA, T is used. 2 As a monitoring statistic, the statistic can be given by the following formula:

[0111]

[0112] in, and represent time k The i-th element.

[0113] Step 1.2: Calculate T 2 To estimate the control limits of the statistic, due to the non-Gaussian distribution of the state variables and residuals, the kernel density estimation (KDE) method is chosen.

[0114] Step Two: Real-time Monitoring;

[0115] First, real-time data is collected and standardized. Then, a real-time statistic T is constructed using a pre-trained JS-DDKCVA model.2 The process status is determined by comparing whether the statistical value is less than the control limit. If T 2 If the value exceeds the control limit, the process is considered to be in an abnormal state; otherwise, the process is considered to be normal and requires no maintenance.

[0116] To verify this invention, we used actual industrial data, taking a steelmaking plant with a volume of 2650 m³. 3 Data samples from blast furnace No. 2 in 2021, containing 28 parameters, were used, with a sampling rate of 10 seconds. Training was performed using 10,000 normal samples, and tests were conducted on two fault conditions: suspended charge and piping failures. Figure 2 and Figure 3 The figure shows the monitoring effect of the method of the present invention on two types of faults. The fault monitoring results show that the model works very well.

[0117] The technical features of the above embodiments can be further combined. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0118] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, all of which fall within the protection scope of the present invention. The protection scope of the present invention is defined by the appended claims and any equivalent technical solutions.

Claims

1. A monitoring method based on Joint Sparse Constraint Data Dependency Kernel Canonical Variable Analysis (JS-DDKCVA), characterized in that, A nonlinear feature extraction framework dependent on blast furnace data is proposed by combining isolated kernel (IK) and principal component analysis (PCA) to obtain data-dependent nonlinear features with discriminative capabilities for fault detection. After extracting the nonlinear features, a method is used... The canonical variable analysis (CVA) method with norm joint sparse constraints is used to further explore the dynamics of the blast furnace ironmaking process. An efficient two-stage iterative alternating direction multiplier method (TPI-ADMM) is designed by combining the manifold-constrained gradient descent (MCGD) method and the gradient hard threshold pursuit (GHTP) method to solve the new optimization objective. Then, the following is employed... Real-time monitoring of the blast furnace ironmaking process using statistical measures and their corresponding control limits; The nonlinear feature extraction framework that relies on blast furnace data is as follows: IK is derived directly from the data by adapting to the local data density structure, and is used to enhance the ability to distinguish between normal and faulty blast furnace samples, as follows: set up For the blast furnace sample dataset; first, extract from the data sample A random sample of n points is taken, and the data space is partitioned using the Venn diagram method with each sample point as a reference; let... Represents the dataset All available partitions A set, where each partition random subset One data point is isolated from the rest of the data points; IK is calculated as any two points. Falling into the same isolation zone Expectations; ； When the condition within the parentheses is met, Based on the Monte Carlo method, the operation of partitioning the data space is repeated independently t times; IK is represented as: ； in Then, the average central kernel matrix is ​​calculated using the following formula. : ； Where the matrix All elements are composed of Composition; In order to extract the main features in the F space, the following eigenvalue decomposition is performed: ； in and Let represent the eigenvalue matrix and eigenvector matrix, respectively; then, the nonlinear eigenma matrix Z, containing the main information, is given by the n largest eigenvalues ​​and their corresponding orthogonal eigenvectors. , 。 2. The method according to claim 1, characterized in that, Integrate the obtained nonlinear features into The new optimization objective proposed in the canonical variable analysis (CVA) of norm joint sparse constraints is: First, JS-DDKCVA will use the data-dependent nonlinear feature matrix. Divided into the past Hankel matrix And the future Hankel matrix The goal of the model is to find a pair of joint sparse canonical matrices J and L such that and To maximize the correlation between them, the model is constructed as follows: ； ； in, , This represents the regularization parameter, where r is the number of regularization variables, and represent Norm, Norm is Norm and Combinations of norms are calculated as follows: ； in Indicates the cardinality.

3. The method according to claim 1, characterized in that, The efficient two-stage iterative alternating direction multiplier method (TPI-ADMM) designed by combining the manifold-constrained gradient descent (MCGD) method and the gradient hard threshold pursuit (GHTP) method is as follows: If L is fixed, then the following optimization problem is obtained: ； ； When J is fixed, the optimization problem for solving L is: ； ； The solution to J and L is obtained by alternating iterations in two stages until J and L converge. Solving for J involves introducing auxiliary variables. and make The optimization problem can be written in the form of an augmented Lagrangian function as follows: ； Where W represents the Lagrange multiplier. This represents the penalty parameter, which requires A to satisfy the constraint. The Alternating Direction Multiplier Method (ADMM) is applied to solve the problem in the order of optimization of A, J, W. To solve subproblem A, the optimization problem simplifies to the following form: ； ； When A and W are fixed, the J subproblem becomes: ； set up Next, the GHTP algorithm can be used to solve for L; After J and L are determined, W is calculated using the following formula: ； Following the above operations, the dynamic projection matrix J with joint sparse constraints is obtained. Then, the data-related blast furnace nonlinear eigenvectors are transformed into q-dimensional regularized variables. This variable is considered to contain essential information that helps monitor the blast furnace ironmaking process. 。 4. The method according to claim 1, characterized in that, The process is as follows: Step 1: Offline modeling; Step 1.1: In the fault detection method based on JS-DDKCVA, use As a monitoring statistic, the statistic is given by the following formula: ； in, and represent time k The i-th element; Step 1.2: Calculation To estimate the control limits of the statistic, due to the non-Gaussian distribution of the state variables and residuals, the kernel density estimation (KDE) method is chosen. Step Two: Real-time Monitoring; First, real-time data is collected and standardized. Then, real-time statistics are constructed using a pre-trained JS-DDKCVA model. The process operating status is determined by comparing whether the statistical value is less than the control limit; if... If the value exceeds the control limit, the process is considered to be in an abnormal state; otherwise, the process is considered to be normal and requires no maintenance.

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