A method for monitoring the operating status of a decarbonization device using a multi-block nonlinear mapping strategy

Abstract

The present invention discloses a method for monitoring the operating status of a decarbonization device using a multi-block nonlinear mapping strategy, which aims to solve the problem of how to implement explicit nonlinear mapping for the sampling data of the decarbonization device in the synthetic ammonia process to describe the nonlinear relationship, and on this basis, adaptively extract the features that are most beneficial to the implementation of operating status monitoring in real time, thereby effectively implementing the operating status monitoring of the decarbonization device. Compared with traditional methods, the method of the present invention adopts an explicit third-order nonlinear mapping to describe the nonlinear relationship between each measurement variable, and divides it into blocks according to different orders. Secondly, the method of the present invention involves the use of a new online multi-block abnormal feature analysis technology to adaptively obtain the corresponding load vector for different online sampling data, thereby analyzing and extracting the abnormal features of different sub-blocks, and always ensuring that the extracted sub-block features are the most representative of abnormal changes.

Description

Technical Field

[0001] The present invention relates to a method for monitoring the operating status of a chemical process, and in particular to a method for monitoring the operating status of a decarbonization device using a multi-block nonlinear mapping strategy. Background Art

[0002] With the growing momentum of economic globalization, global market competition is intensifying. This has led to higher demands on the quality of process industry products, industrial process safety, production efficiency, rational production structure, and energy consumption. Ammonia is a key inorganic chemical product and plays a vital role in the national economy. In the synthetic ammonia production process, raw materials such as coke, coal, coke oven gas, natural gas, naphtha, heavy oil, and feed gas (semi-water gas) are purified and refined (primarily hydrogen and nitrogen) before being compressed to a specific pressure. The compressed gas then enters the ammonia synthesis tower, where it is heated at high temperatures and under the action of a catalyst to produce ammonia and other by-products. Due to the low conversion rate of ammonia synthesis and the high energy consumption per unit of product, ensuring the stability of the synthetic ammonia process is a crucial technical measure to ensure the ammonia content in the product.

[0003] The ammonia decarbonization unit is a crucial step in the ammonia production process. Its primary function is to eliminate as much carbon dioxide as possible from the raw process gas. The unit absorbs carbon dioxide from the synthesis gas and reduces the power consumption of the synthesis gas compressor within a reasonable range. Therefore, the performance of the decarbonization unit is a bottleneck in the ammonia synthesis process system and is directly related to the stable operation of the entire system. With the continuous development of the modern processing industry and advancements in data acquisition technology, it has become easier to acquire data such as temperature, pressure, and flow during the production process in distributed control systems (DCSs) that collect and store large amounts of industrial process data. This has laid a solid foundation for implementing data-driven monitoring of the decarbonization unit's operating status.

[0004] However, the data measured by sensors in ammonia decarbonization units exhibit significant nonlinear variations. Directly modeling this data using linear models is hampered by the nonlinear relationships between the data, resulting in sluggish operational status monitoring. To address the nonlinear relationships between measured variables, nonlinear modeling techniques based on kernel methods have been widely used in operational status monitoring. However, a typical problem with kernel methods is that the functions describing nonlinear relationships are all hidden unknowns, making the data models constructed using kernel methods uninterpretable. Furthermore, kernel-based data modeling extracts features hidden in normal operating data, and the goal of this feature extraction is not directly for operational status monitoring. Therefore, extracting features that are directly beneficial to operational status monitoring is the key to effectively monitoring the proper operation of decarbonization units. Summary of the Invention

[0005] The main technical problem to be solved by the present invention is: how to implement explicit nonlinear mapping for the sampled data of the decarbonization device to describe the nonlinear relationship, and on this basis, adaptively extract in real time the features that are most beneficial for implementing operational status monitoring, thereby effectively implementing the operational status monitoring of the decarbonization device. Specifically, the method of the present invention first expands the dimension of the original sampled data through a third-order polynomial mapping, and then combines nonlinear mappings of different orders into a corresponding data block. Next, online feature analysis is performed using the latest sampled data, and monitoring indicators are calculated using the real-time updated load vector, thereby completing the real-time monitoring task of whether the synthetic ammonia decarbonization device is operating normally.

[0006] The technical solution adopted by the method of the present invention to solve the above problems is: a method for monitoring the operating status of a decarbonization device using a multi-block nonlinear mapping strategy, comprising the following steps:

[0007] Step (1): Obtain N sets of sampling data x1, x2, ..., x2 from the DCS database of the decarbonization unit under normal operation. N ; where x i ∈R 10×1 Represents the i-th group of sampled data, with subscript i∈{1,2,…,N}, R 10×1 represents a 10×1 dimensional real number vector. Each set of sampling data is a 10×1 dimensional real number vector composed of 10 sample data. The arrangement order of these 10 sample data is: inlet flow rate, inlet temperature, separator temperature, separator pressure, absorption tower liquid level, absorption tower temperature, absorption tower pressure, absorption tower top outlet flow rate, outlet temperature, and outlet flow rate.

[0008] Step (2): For N groups of sample data x1, x2, ..., x N Implement the third-order nonlinear polynomial mapping respectively to obtain the first-order mapping matrix X1, the second-order mapping matrix X2, the second-order cross matrix X3, the third-order mapping matrix X4, and the third-order cross matrix X5. The specific implementation process is shown in steps (2.1) to (2.9).

[0009] Step (2.1): Set the first-order mapping matrix X1 = [x1, x2, ..., x N ] T Then, let m1, m2, ..., m 10 In turn, it represents the i-th group of sample data x i The 10 sample data in ; where the superscript T represents the transpose of the matrix or vector.

[0010] Step (2.2): According to the formula Constructing a second-order mapping vector Then, set the i-th row vector in the second-order mapping matrix X2 equal to

[0011] Step (2.3): According to the formula Constructing a third-order mapping vector Then, set the i-th row vector in the third-order mapping matrix X4 equal to

[0012] Step (2.4): After initializing j = 1, initialize the second-order cross vector and the third-order cross vector

[0013] Step (2.5): Determine whether j is less than 9; if so, set j = j + 1 and use the formula renew Then execute step (2.6); if not, execute step (2.6) directly.

[0014] Step (2.6): Determine whether j+1 is equal to 10; if so, according to the formula renew Then, execute step (2.7); if not, then according to the formula renew Then proceed to step (2.7).

[0015] Step (2.7): Determine whether j+1 is equal to 10; if not, return to step (2.5); if so, execute step (2.8).

[0016] Step (2.8): Set the i-th row vector in the second-order cross matrix X3 to be equal to Set the i-th row vector in the third-order cross matrix X5 to be equal to

[0017] Step (2.9): When i is equal to 1, 2,…, N respectively, repeat steps (2.2) to (2.8) to obtain the second-order mapping matrix X2, the second-order cross matrix X3, the third-order mapping matrix X4, and the third-order cross matrix X5.

[0018] Step (3): According to the formula The column vectors of each column in X1, X2, ..., X5 are standardized to obtain 5 reference sub-block matrices in, Represents X b The column vector of the kth column in , express The column vector of the kth column in , and Represents column vectors The mean and standard deviation of all elements in , b∈{1,2,3,4,5}. That is: when b is equal to 1,2,3,4,5 respectively, X b are equivalent to X1, X2, …, X5, respectively, and are equivalent to

[0019] Step (4): According to the formula and After calculating the matrices L1, L2, L3, L4 and L5, singular value decomposition is performed on L1, L2, L3, L4 and L5 respectively, thereby obtaining the corresponding unitary matrices U1, U2, ..., U5 and singular value diagonal matrices V1, V2, ..., V5, and according to the formula Calculate the matrices separately

[0020] Step (5): For the reference sub-block matrix Each row vector in the performs online multi-block abnormal feature analysis, thereby calculating the corresponding N monitoring indicators Q1, Q2, ..., Q N Then determine the upper control limit Q of the monitoring indicator lim The specific implementation process is shown in steps (5.1) to (5.6).

[0021] Step (5.1): After initializing i=1, set the online sub-block vectors y1, y2, ..., y5 to be equal to The i-th row vector in , that is: set the online sub-block vector y1 equal to The i-th row vector in the y-th row, set the online sub-block vector y2 equal to The i-th row vector in , and so on.

[0022] Step (5.2): When b is equal to 1, 2, 3, 4, and 5 respectively, solve the eigenvalue problem G b g b =λ b g b The largest eigenvalue λ b The corresponding eigenvector g b Then, according to Calculate the sub-block load vector w b ; Among them, the matrix

[0023] Step (5.3): According to the formula After normalizing the sub-block load vectors w1, w2, ..., w5, they are merged into a load vector p = [w1 T ,w2 T ,…,w5 T ]T .

[0024] Step (5.4): Merge the online sub-block vectors y1, y2, ..., y5 into a nonlinear extended vector y = [y1, y2, ..., y5] T Then, through the formula Q i =y T pp T y calculates the corresponding monitoring index Q i .

[0025] Step (5.5): Determine whether i is less than N; if so, set i = i + 1, and set the online sub-block vectors y1, y2, ..., y5 to be equal to The i-th row vector in , and return to step (5.2); if not, then get N monitoring indicators Q1, Q2, ..., Q N .

[0026] Step (5.6): For Q1, Q2, ..., Q N Kernel Density Estimation (KDE) is performed to obtain the confidence limit Q at a confidence level of α = 99.5%. KDE , and Q1,Q2,…,Q N The average value of the largest ξ values ​​is recorded as Q AVG Finally, determine the upper control limit Q of the monitoring indicator lim =max{Q KDE ,Q AVG}; where ξ represents the largest integer not greater than N×99%, max{Q KDE ,Q AVG} means taking Q KDE and Q AVG The maximum value in .

[0027] It should be noted that the implementation process of the above steps (4) and (5) is actually an online multi-block abnormal feature analysis algorithm based on nonlinear extended vectors designed by the method of the present invention, whose goal is to extract the online sub-block vectors y1, y2, ..., y5 relative to the reference sub-block matrix through the sub-block load vectors w1, w2, ..., w5. The abnormal characteristics are:

[0028]

[0029] Considering that each sub-block is relatively independent, the above equation (1) can be transformed into the following constrained optimization problem without loss of generality:

[0030]

[0031] In the above formula, b∈{1,2,…,5}, the target value in formula ① is equal to the sum of the target values ​​in the five formulas ②. The above formula ② can be optimized and solved by the classic Lagrange multiplier method. It is necessary to first use the Lagrange coefficient λ b Constructing the Lagrangian function Then calculate J b Relative to w b The partial derivative of , that is:

[0032]

[0033] When the above formula ③ is equal to 0, the objective function in the above formula ② takes the extreme value, so we can get If we multiply both sides of the equation by w on the left b T , we can get the equation relationship: Therefore, the maximum eigenvalue λ b That is, it is equal to the target value that needs to be solved.

[0034] Taking into account There may be singular values, the matrix L b It is symmetric but not reversible. Therefore, when solving the maximum generalized eigenvalue, it is necessary to follow steps (A) to (C) as shown below to implement the solution.

[0035] Step (A): Matrix L b After performing singular value decomposition and retaining non-zero singular values, the corresponding unitary matrix U is obtained b and the singular value diagonal matrix V b .

[0036] Step (B): According to the formula Calculate the matrix G b Then solve G b Maximum eigenvalue λ b The corresponding eigenvector g b ;in,

[0037] Step (C): Pass Calculate the sub-block load w b .

[0038] The above steps (A) to (C) require the use of matrix This is the same as the matrix in step (4) above. This is the reason for implementing singular value decomposition. In addition, step (B) is equivalent to the implementation process of solving the eigenvector corresponding to the maximum eigenvalue in step (5.2) above.

[0039] Step (6): At the latest sampling time t, use the ammonia process DCS to obtain 10 sample data m1, m2, ..., m of the ammonia decarbonization unit. 10 Then, a third-order nonlinear polynomial mapping is performed on it to obtain a first-order mapping vector Second-order mapping vector Second-order cross vector Third-order mapping vector and the third-order cross vector The specific implementation process is shown in steps (6.1) to (6.5).

[0040] Step (6.1): According to the method and Form the first-order mapping vectors respectively Second-order mapping vector and the third-order mapping vector Then, initialize j=1.

[0041] Step (6.2): ​​Initialize the second-order cross vector Initialize the third-order cross vector

[0042] Step (6.3): Determine whether the condition j < 9 is met; if so, set j = j + 1 and then use the formula renew Then execute step (6.4); if not, execute step (6.4) directly.

[0043] Step (6.4): Determine whether j+1 is equal to 10; if so, according to the formula renew Then, execute step (6.5); if not, then according to the formula renew Then proceed to step (6.5).

[0044] Step (6.5): Determine whether j+1 is equal to 10; if not, return to step (6.3); if so, get

[0045] Step (7): Using the average and standard deviation By formula right The elements of each row in are standardized and updated to obtain the online sub-block vectors y1, y2, ..., y5; and y b (k) respectively represent and y b The kth element in .

[0046] Step (8): Perform online multi-block anomaly feature analysis on y1, y2,…, y5 through steps (5.2) to (5.3) to obtain the load vector p.

[0047] Step (9): Merge the online sub-block vectors y1, y2, ..., y5 into a nonlinear extended vector y = [y1, y2, ..., y5] T Then, according to the formula Q t =y T pp T y calculates the monitoring index Q at the latest sampling time t , and judge Q t Is it greater than Q lim ; If not, the decarbonization device is operating normally, and return to step (6) to continue using the 10 sample data at the latest sampling time to implement operation status monitoring; if so, execute step (10) to decide whether to trigger an abnormal alarm.

[0048] Step (10): Return to step (6) and continue to use the sample data at the latest sampling moment to implement the operation status monitoring. If the monitoring indicators at consecutive A sampling moments are greater than Q lim , an abnormal alarm is triggered; otherwise, the decarbonization device operates normally; where A is equal to the quotient of the shortest time required to trigger an abnormal alarm divided by the sampling interval.

[0049] Through the above-mentioned implementation steps, the advantages of the method of the present invention are introduced as follows.

[0050] First, the method of the present invention employs an explicit third-order nonlinear mapping to describe the nonlinear relationships between the measured variables, and processes them in blocks according to different orders. Second, the method of the present invention utilizes a novel online multi-block abnormal feature analysis technique to adaptively acquire corresponding load vectors for different online sampled data, thereby analyzing and extracting abnormal features from different sub-blocks. This method can effectively address the nonlinearity of the sampled data from the synthetic ammonia decarbonization unit and consistently ensure that the extracted sub-block features are the most representative of abnormal changes. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 Schematic diagram of the implementation process of the method of the present invention.

[0052] Figure 2 A detailed diagram showing whether the monitoring indicators are abnormal or not. DETAILED DESCRIPTION

[0053] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0054] The present invention discloses a method for monitoring the operating status of a decarbonization device using a multi-block nonlinear mapping strategy. Figure 1 The implementation flow diagram shown and sampling data of a domestic ammonia synthesis process are used to illustrate the specific implementation method of the method of the present invention.

[0055] Step (1): Obtain N sets of sampling data x1, x2, ..., x2 from the DCS database of the synthetic ammonia process when the synthetic ammonia decarbonization unit is operating under normal conditions. N .

[0056] Step (2): For N groups of sample data x1, x2, ..., x N The third-order nonlinear polynomial mapping is implemented respectively to obtain the first-order mapping matrix X1, the second-order mapping matrix X2, the second-order cross matrix X3, the third-order mapping matrix X4, and the third-order cross matrix X5. The specific implementation process is shown in the above steps (2.1) to (2.9).

[0057] Step (3): According to the formula The column vectors of each column in X1, X2, ..., X5 are standardized to obtain 5 reference sub-block matrices

[0058] Step (4): For each matrix and After performing singular value decomposition to obtain unitary matrices U1, U2, ..., U5 and singular value diagonal matrices V1, V2, ..., V5, we can use the formula Calculate the matrices separately

[0059] Step (5): For the reference sub-block matrix Each row vector in the performs online multi-block abnormal feature analysis, thereby calculating the corresponding N monitoring indicators Q1, Q2, ..., Q N Then determine the upper control limit Q of the monitoring indicator lim The specific implementation process is shown in the above steps (5.1) to (5.6).

[0060] Step (6): At the latest sampling time t, use the ammonia process DCS to obtain 10 sample data m1, m2, ..., m of the ammonia decarbonization unit. 10 Then, a third-order nonlinear polynomial mapping is applied to it to obtain

[0061] Step (7): Using the average and standard deviation By formula right The elements of each row in are normalized to obtain the online sub-block vectors y1, y2, ..., y5.

[0062] Step (8): Perform online multi-block anomaly feature analysis on y1, y2,…, y5 through steps (5.2) to (5.3) to obtain the load vector p.

[0063] Step (9): Merge the online sub-block vectors y1, y2, ..., y5 into a nonlinear extended vector y = [y1, y2, ..., y5] T Then, according to the formula Q t =y T pp T y calculates the monitoring index Q at the latest sampling time t , and judge Q t Is it greater than Q lim If not, the synthetic ammonia decarbonization device is operating normally, and the process returns to step (6) to continue monitoring the operating status using the 10 sample data at the latest sampling time; if so, step (10) is executed to determine whether to trigger an abnormal alarm;

[0064] Step (10): Return to step (6) and continue to use the sample data at the latest sampling moment to implement the operation status monitoring. If the monitoring indicators at consecutive A sampling moments are greater than Q lim , an abnormal alarm is triggered; otherwise, the synthetic ammonia decarbonization device operates normally.

[0065] Draw the image in chronological order according to the monitoring indicators at each new sampling moment, and lim Also plotted as the upper control limit Figure 2 In. From Figure 2 Q t The change of Q can be seen directly. t The curve is located at Q lim If it is above, it means that an abnormality has occurred; otherwise, it means that the synthetic ammonia decarbonization unit is operating normally.

Claims

1. A method for monitoring the operating status of a decarbonization device using a multi-block nonlinear mapping strategy, characterized in that: The specific steps include the following: Step (1): Obtain N sets of sampling data x1, x2, ..., x2 from the DCS database of the decarbonization unit under normal operation. N ; where x i ∈R 10×1 Represents the i-th group of sampled data, with subscript i∈{1,2,…,N}, R 10×1 represents a 10×1 dimensional real number vector. Each set of sampling data is a 10×1 dimensional real number vector consisting of 10 sample data. The order of arrangement of these 10 sample data is: inlet flow rate, inlet temperature, separator temperature, separator pressure, absorption tower liquid level, absorption tower temperature, absorption tower pressure, absorption tower top outlet flow rate, outlet temperature, outlet flow rate; Step (2): For N groups of sample data x1, x2, ..., x N Implement the third-order nonlinear polynomial mapping respectively to obtain the first-order mapping matrix X1, the second-order mapping matrix X2, the second-order cross matrix X3, the third-order mapping matrix X4, and the third-order cross matrix X5. The specific implementation process is shown in steps (2.1) to (2.9); Step (2.1): Set the first-order mapping matrix X1 = [x1, x2, ..., x N ] T Then, let m1, m2, ..., m 10 In turn, it represents the i-th group of sample data x i The 10 sample data in ; where the superscript T represents the transpose of the matrix or vector; Step (2.2): According to the formula Constructing a second-order mapping vector Then, set the i-th row vector in the second-order mapping matrix X2 equal to Step (2.3): According to the formula Constructing a third-order mapping vector Then, set the i-th row vector in the third-order mapping matrix X4 equal to Step (2.4): After initializing j = 1, initialize the second-order cross vector and the third-order cross vector Step (2.5): Determine whether j is less than 9; if so, set j = j + 1 and use the formula renew Then execute step (2.6); if not, execute step (2.6) directly; step (2.6): determine whether j+1 is equal to 10; if so, according to the formula renew Then, execute step (2.7); if not, then according to the formula renew Then, proceed to step (2.7); Step (2.7): Determine whether j+1 is equal to 10; if not, return to step (2.5); if so, execute step (2.8); Step (2.8): Set the i-th row vector in the second-order cross matrix X3 to be equal to Set the i-th row vector in the third-order cross matrix X5 to be equal to Step (2.9): When i is equal to 1, 2, ..., N, respectively, repeat steps (2.2) to (2.8) to obtain the second-order mapping matrix X2, the second-order cross matrix X3, the third-order mapping matrix X4, and the third-order cross matrix X5; Step (3): According to the formula The column vectors of each column in X1, X2, ..., X5 are standardized to obtain 5 reference sub-block matrices in, Represents X b The column vector of the kth column in , express The column vector of the kth column in , and Represents column vectors The mean and standard deviation of all elements in , b∈{1,2,3,4,5}; Step (4): According to the formula and After calculating the matrices L1, L2, L3, L4 and L5, singular value decomposition is performed on L1, L2, L3, L4 and L5 respectively, thereby obtaining the corresponding unitary matrices U1, U2, ..., U5 and singular value diagonal matrices V1, V2, ..., V5, and according to the formula Calculate the matrices separately Step (5): For the reference sub-block matrix Each row vector in the performs online multi-block abnormal feature analysis, thereby calculating the corresponding N monitoring indicators Q1, Q2, ..., Q N Then determine the upper control limit Q of the monitoring indicator lim , the specific implementation process is shown in steps (5.1) to (5.6); Step (5.1): After initializing i=1, set the online sub-block vectors y1, y2, ..., y5 to be equal to The i-th row vector in ; Step (5.2): When b is equal to 1, 2, 3, 4, and 5 respectively, solve the eigenvalue problem G b g b =λ b g b The largest eigenvalue λ b The corresponding eigenvector g b Then, according to Calculate the sub-block load vector w b ; Among them, the matrix Step (5.3): According to the formula After normalizing the sub-block load vectors w1, w2, ..., w5, they are merged into a load vector p = [w1 T ,w2 T ,…,w5 T ] T ; Step (5.4): Merge the online sub-block vectors y1, y2, ..., y5 into a nonlinear extended vector y = [y1, y2, ..., y5] T Then, through the formula Q i =y T pp T y calculates the corresponding monitoring index Q i ; Step (5.5): Determine whether i is less than N; if so, set i = i + 1, and set y1, y2, ..., y5 to be equal to The i-th row vector in , and return to step (5.2); if not, then get N monitoring indicators Q1, Q2, ..., Q N ; Step (5.6): For Q1, Q2, ..., Q N Implement kernel density estimation to obtain the confidence limit Q at confidence level α = 99.5% KDE , and Q1,Q2,…,Q N The average value of the largest ξ values ​​is recorded as Q AVG Then determine the upper control limit Q of the monitoring indicator lim =max{Q KDE ,Q AVG }; where ξ represents the largest integer not greater than N×99%, max{Q KDE ,Q AVG } means taking Q KDE and Q AVG The maximum value in ; Step (6): At the latest sampling time t, use the ammonia process DCS to obtain 10 sample data m1, m2, ..., m of the ammonia decarbonization unit. 10 Then, a third-order nonlinear polynomial mapping is performed on it to obtain a first-order mapping vector Second-order mapping vector Second-order cross vector Third-order mapping vector and the third-order cross vector Step (7): Using the average and standard deviation By formula right The elements of each row in are standardized and updated to obtain the online sub-block vectors y1, y2, ..., y5; and y b (k) respectively represent and y b The kth element in ; Step (8): Perform online multi-block anomaly feature analysis on y1, y2, ..., y5 through steps (5.2) to (5.3) to obtain the load vector p; Step (9): Merge the online sub-block vectors y1, y2, ..., y5 into a nonlinear extended vector y = [y1, y2, ..., y5] T Then, according to the formula Q t =y T pp T y calculates the monitoring index Q at the latest sampling time t , and judge Q t Is it greater than Q lim If not, the decarbonization device is operating normally, and the process returns to step (6) to continue monitoring the operating status using the 10 sample data at the latest sampling time; if so, step (10) is executed to determine whether to trigger an abnormal alarm; Step (10): Return to step (6) and continue to use the sample data at the latest sampling moment to implement the operation status monitoring. If the monitoring indicators at consecutive A sampling moments are greater than Q lim , an abnormal alarm is triggered; otherwise, the synthetic ammonia decarbonization device operates normally; where A is equal to the quotient of the shortest time required to trigger an abnormal alarm divided by the sampling interval time.

2. A method for monitoring the operating status of a decarbonization device using a multi-block nonlinear mapping strategy according to claim 1, characterized in that: The specific implementation process of step (6) is as follows: Step (6.1): According to the method and Form the first-order mapping vectors respectively Second-order mapping vector and the third-order mapping vector Then, initialize j=1; Step (6.2): ​​Initialize the second-order cross vector Initialize the third-order cross vector Step (6.3): Determine whether the condition j < 9 is met; if so, set j = j + 1 and then use the formula renew Then execute step (6.4); if not, directly execute step (6.4); Step (6.4): Determine whether j+1 is equal to 10; if so, according to the formula renew Then, execute step (6.5); if not, then according to the formula renew Then proceed to step (6.5); Step (6.5): Determine whether j+1 is equal to 10; if not, return to step (6.3); if so, get

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