CN110442991B - Dynamic sulfur recovery soft measurement modeling method based on parameterized FIR (finite Impulse response) model - Google Patents
Dynamic sulfur recovery soft measurement modeling method based on parameterized FIR (finite Impulse response) model Download PDFInfo
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- NINIDFKCEFEMDL-UHFFFAOYSA-N Sulfur Chemical compound [S] NINIDFKCEFEMDL-UHFFFAOYSA-N 0.000 title claims abstract description 67
- 229910052717 sulfur Inorganic materials 0.000 title claims abstract description 67
- 239000011593 sulfur Substances 0.000 title claims abstract description 67
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- B01D53/00—Separation of gases or vapours; Recovering vapours of volatile solvents from gases; Chemical or biological purification of waste gases, e.g. engine exhaust gases, smoke, fumes, flue gases, aerosols
- B01D53/34—Chemical or biological purification of waste gases
- B01D53/74—General processes for purification of waste gases; Apparatus or devices specially adapted therefor
- B01D53/86—Catalytic processes
- B01D53/8603—Removing sulfur compounds
- B01D53/8612—Hydrogen sulfide
- B01D53/8615—Mixtures of hydrogen sulfide and sulfur oxides
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
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Abstract
The invention discloses a dynamic sulfur recovery soft measurement modeling method based on a parameterized FIR model, which comprises the steps of collecting a variable sequence of a sulfur recovery process at a fixed sampling frequency, using the variable sequence for model parameter optimization, and setting a model hyper-parameter; constructing a model structure according to the set hyper-parameters, and initializing model parameters; training an optimization model; model prediction; the variable sequence is divided into an auxiliary variable and a main variable; the model of the invention considers the time sequence information of the sulfur recovery process, and can effectively avoid the over-fitting phenomenon, thereby ensuring the prediction precision and further ensuring the normal operation of closed-loop control by means of a soft measurer before the sensor is aged or damaged.
Description
Technical Field
The invention relates to the technical field of sulfur recovery process soft measurement modeling and application, in particular to a dynamic sulfur recovery soft measurement modeling method based on a parameterized FIR model.
Background
The sulfur recovery unit is a device for removing sulfide in the exhaust gas, and the gas entering the device has two types, one is rich in hydrogen sulfide gas and is called MEA, and the other is rich in hydrogen sulfide and sulfur dioxide gas and is called SWS; the gas is first sent to B106, B103 (which is a separation chamber with excess air) for incineration to remove residual ammonia, as shown in the following formula,
then sent to catalytic converters E101 to E103; catalytic converter pass H2S and SO2The reaction of (A) to produce water and pure sulfur, thereby achieving the purpose of removing sulfide, as shown in the following formula,
when H is present2S and SO2The molar concentration ratio of (A) to (B) is 2:1, and in order to remove sulfides more completely, H in the tail gas needs to be fully reacted2S and SO2The concentration is measured in real time to form closed-loop control; however, the on-line concentration sensor is easily corroded by acid gas, and the sulfur recovery process is a continuous process, so that a soft measurer is needed to ensure normal operation of closed-loop control when the sensor is aged or damaged, but the closed-loop control cannot be normally used due to aging or damage of the sensor in the current sulfur recovery process, so that the content of sulfide cannot be monitored in real time, and the use is unreliable.
In soft measurement modeling, a neural network is the most common nonlinear model, and generally used neural network models have a chain structure, the structure of the chain structure can be regarded as series connection of multiple layers of functions, each layer of function can be regarded as being composed of multiple nodes, the model structure is originally derived from simulation of a biological nervous system, and in soft measurement modeling, the neural network model is more regarded as a universal fitter for nonlinear relations.
The FIR filter (finite long single-bit impulse response filter) is a non-recursive filter, and is commonly used for solving the problem of auxiliary variable measurement noise or dynamic response in soft measurement modeling, however, at present, FIR parameters are usually given by semi-experience, the semi-experience design method reduces the number of parameters, but also limits the flexibility of the model, and when the problem of feature extraction is relatively complex (for example, auxiliary variables are affected by dynamic response and observation noise at the same time), the effectiveness of feature extraction is limited by the semi-experience given determination of the FIR layer.
Disclosure of Invention
This section is for the purpose of summarizing some aspects of embodiments of the invention and to briefly introduce some preferred embodiments. In this section, as well as in the abstract and the title of the invention of this application, simplifications or omissions may be made to avoid obscuring the purpose of the section, the abstract and the title, and such simplifications or omissions are not intended to limit the scope of the invention.
The invention is provided in view of the problem of how to ensure the normal use of closed-loop control when a sensor is aged or damaged in the conventional method for controlling the closed-loop control of sulfur recovery by dynamic sulfur recovery soft measurement modeling.
Therefore, the invention aims to provide a dynamic sulfur recovery soft measurement modeling method based on a parameterized FIR model, so as to ensure the normal operation of closed-loop control by means of a soft measurer before the sensor is aged or damaged.
In order to solve the technical problems, the invention provides the following technical scheme: a dynamic sulfur recovery soft measurement modeling method based on a parameterized FIR model comprises,
in the sulfur recovery process, a sensor is adopted and the tail gas is measured and collected in real time at a fixed sampling frequency to obtain a variable sequence of the sulfur recovery process;
using the variable sequence for model parameter optimization, and setting model hyper-parameters;
constructing a model structure according to the set hyper-parameters, and initializing model parameters;
training an optimization model;
model prediction;
the variable sequence is divided into an auxiliary variable and a main variable;
wherein the hyper-parameters comprise a length of the FIR and a width of the model hidden layer.
As a preferable scheme of the dynamic sulfur recovery soft measurement modeling method based on the parameterized FIR model, the method comprises the following steps: the sensor is divided into a solid metal oxide semiconductor sensor and a gas flow sensor, and the solid metal oxide semiconductor sensor is used for detecting tail gas H2S and SO2The concentration is collected in real time measurements and the GAS flow sensors collect the MEA _ GAS flow, AIR _ MEA AIR flow, AIR _ MEA _2 secondary AIR flow, SWS zone GAS flow, and SWS zone AIR flow.
As a preferable scheme of the dynamic sulfur recovery soft measurement modeling method based on the parameterized FIR model, the method comprises the following steps: the model parameter initialization is by the following formula:
wherein lLRepresenting a full one vector of dimension L,/L+1And
respectively represent dimensions L +1 and m(2)All one vectors of (a);
and
representing parameters contained in a second layer of the model, and respectively representing the connection weight and the threshold value of the second layer;
a representation matrix W(2)The ith row and the jth column of (1); l represents the length of the FIR; m represents the dimension of the auxiliary variable, m(2)Representing the width of the model hidden layer; the superscript T denotes the transpose of the matrix or vector, W(1)The representation is a model first layer parameter, representing the weight coefficients of the FIR,
means 1 line m(2)The set of real transverse quantities of a column,
means m rows m(2)A set of real matrices for a column.
As a preferable scheme of the dynamic sulfur recovery soft measurement modeling method based on the parameterized FIR model, the method comprises the following steps: the step of training the optimization model comprises:
inputting a sampling sequence of an auxiliary variable and a main variable in the sulfur recovery process, and simultaneously setting iteration times and training step length of parameter optimization;
calculating forward propagation of the model to obtain a sequence;
calculating the back propagation of the model to obtain the derivatives of the first and second layer parameters with respect to the cost function J;
optimizing the model parameters according to an Adam algorithm;
judging whether the iteration times are reached;
and updating the parameters of the output layer.
As a preferable scheme of the dynamic sulfur recovery soft measurement modeling method based on the parameterized FIR model, the method comprises the following steps: inputting sulfur recovery process auxiliary variables, and calculating a constant matrix C belonging to RL×mAnd D ∈ RL×L×m；
Wherein the calculation constant matrix is obtained by the following formula:
wherein U represents a sample sequence of auxiliary variables; c represents a constant matrix; d denotes a constant tensor; c:,iThe ith column vector of the matrix C represents the mean value sequence of the ith auxiliary variable;
and
respectively represent the t-th matrix C1Rows ith and tth2The element corresponding to line i;
representing the three-dimensional tensor Dth1Line t2The element corresponding to the ith block of the column represents the ith auxiliary variable t1Time value and t2Covariance statistics of time values;
and
respectively representing the ith auxiliary scalar at the t-t1And τ -t2The value of the variable at the moment; n represents the length of the input sequence; u shape(n:1),i＝[Un,i,Un-1,i,…,U1,i]，Uj,iThe element corresponding to the jth row and ith column of the matrix U; n represents a dimension; lNRepresenting a full row vector of dimension N; "+" denotes discrete finite convolution operation, RL×L×mSet of real tensor, R, referring to L blocks, L rows and m columnsL×mRefers to a set of real matrices of L rows and m columns.
As a preferable scheme of the dynamic sulfur recovery soft measurement modeling method based on the parameterized FIR model, the method comprises the following steps: the step of calculating the forward propagation of the model to obtain the sequence comprises the following steps:
filtering the auxiliary variable by using the FIR parameter;
carrying out layer normalization operation;
calculating an output sequence of the hidden layer;
and solving the average value of the second layer output sequence and normalizing the sequence.
As a preferable scheme of the dynamic sulfur recovery soft measurement modeling method based on the parameterized FIR model, the method comprises the following steps: the FIR parameter filters the auxiliary variable by adopting the following formula:
wherein H(1)As output results of the first layer of the model, W(1)∈RL×mIs a parameter matrix of the FIR layer;
represents the output sequence H(1)Column i, U:,iAnd
respectively representing matrices U and W(1)The ith column vector of (1).
As a preferable scheme of the dynamic sulfur recovery soft measurement modeling method based on the parameterized FIR model, the method comprises the following steps: the layer normalization operation is performed according to the following formula:
wherein the content of the first and second substances,
and
respectively represent column vectors
The mean and variance of; d:,:,iRepresenting a matrix corresponding to the ith block of the three-dimensional tensor Dith;
is a vector
The result after normalization; lNRepresenting a full row vector of dimension N; c:,i TRepresents a column vector C:,iTransposing; w:,i (1)A representation matrix W(1)The ith column vector of (1); lNRepresenting a full row vector of dimension N; xi denotes a constant parameter, RL×mRefers to a set of real matrices of L rows and m columns.
As a preferable scheme of the dynamic sulfur recovery soft measurement modeling method based on the parameterized FIR model, the method comprises the following steps: the step of calculating the back propagation of the model to obtain the derivatives of the first and second layer parameters with respect to the cost function J comprises the following steps:
obtaining the optimal value of the output layer parameter;
and calculating the gradient of the first layer parameter and the second layer parameter layer by layer.
As a preferable scheme of the dynamic sulfur recovery soft measurement modeling method based on the parameterized FIR model, the method comprises the following steps: the model predicts:
inputting the dominant variable of the test set sample into the model;
and calculating a prediction sequence of the dominant variable according to the forward propagation of the model.
The invention has the beneficial effects that: the model of the invention considers the time sequence information of the sulfur recovery process, and can effectively avoid the over-fitting phenomenon, thereby ensuring the prediction precision and further ensuring the normal operation of closed-loop control by means of a soft measurer before the sensor is aged or damaged.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise. Wherein:
FIG. 1 is a schematic diagram of the overall steps of the dynamic sulfur recovery soft measurement modeling method based on the parameterized FIR model.
FIG. 2 is a schematic structural diagram of a model construction according to the dynamic sulfur recovery soft measurement modeling method based on a parameterized FIR model.
FIG. 3 is a schematic diagram of the steps of the training optimization model of the dynamic sulfur recovery soft measurement modeling method based on the parameterized FIR model.
FIG. 4 is a schematic diagram of the steps of calculating the forward propagation of the model of the dynamic sulfur recovery soft measurement modeling method based on the parameterized FIR model to obtain a sequence.
Fig. 5 is a schematic diagram of the step of obtaining the derivative of the first and second layer parameters with respect to the cost function J by the model back propagation calculation of the dynamic sulfur recovery soft measurement modeling method based on the parameterized FIR model.
FIG. 6 is a schematic diagram of the steps involved in model prediction for the dynamic sulfur recovery soft measurement modeling method based on a parameterized FIR model.
FIG. 7 is a schematic process flow diagram of a sulfur recovery unit of the dynamic sulfur recovery soft measurement modeling method based on a parameterized FIR model according to the present invention.
FIG. 8 is a schematic diagram of the modeling execution of the dynamic sulfur recovery soft measurement modeling method based on the parameterized FIR model.
FIG. 9 is a schematic diagram of the modeling result of GPR of the dynamic sulfur recovery soft measurement modeling method based on the parameterized FIR model.
FIG. 10 is a schematic diagram of the modeling result of the dynamic sulfur recovery soft measurement modeling method based on the parameterized FIR model.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described and will be readily apparent to those of ordinary skill in the art without departing from the spirit of the present invention, and therefore the present invention is not limited to the specific embodiments disclosed below.
Furthermore, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one implementation of the invention. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.
Furthermore, the present invention is described in detail with reference to the drawings, and in the detailed description of the embodiments of the present invention, the cross-sectional view illustrating the structure of the device is not enlarged partially according to the general scale for convenience of illustration, and the drawings are only exemplary and should not be construed as limiting the scope of the present invention. In addition, the three-dimensional dimensions of length, width and depth should be included in the actual fabrication.
Example 1
Referring to fig. 1 and 8, there is provided a schematic overall structure diagram of a method for closed-loop control of sulfur recovery by dynamic sulfur recovery soft measurement modeling, such as fig. 1, the dynamic sulfur recovery soft measurement modeling method based on a parameterized FIR model includes three aspects of model initialization, model parameter optimization and model prediction, including the steps of:
s1: in the sulfur recovery process, a sensor is adopted and the tail gas is measured and collected in real time at a fixed sampling frequency to obtain a variable sequence of the sulfur recovery process;
s2: using the variable sequence for model parameter optimization, and setting model hyper-parameters;
s3: constructing a model structure according to the set hyper-parameters, and initializing model parameters;
s4: training an optimization model;
s5: and (5) model prediction.
Specifically, the main structure of the invention comprises the following steps:
s1: in the sulfur recovery process, a sensor is adopted and the tail gas is measured and collected in real time at a fixed sampling frequency to obtain a variable sequence of the sulfur recovery process; the variable sequence is divided into an auxiliary variable and a main variable, the sensors are divided into a solid metal oxide semiconductor sensor and a gas flow sensor, and the solid metal oxide semiconductor sensor is used for detecting tail gas H2S and SO2The concentration is measured and collected in real time, the GAS flow sensor collects MEA _ GAS GAS flow, AIR _ MEA AIR flow, AIR _ MEA _2 secondary AIR flow, SWS area GAS flow and SWS area AIR flow, and the tail GAS H2S and SO2Concentration as the dominant variable, while MEA _ GAS flow, AIR _ MEA AIR flow, AIR _ MEA _2 secondary AIR flow, SWS zone GAS flow, and SWS zone AIR flow are auxiliary variables in the sulfur recovery process with fixed sampling frequency of 1 minute, 2 minutes, or 3 minutes, etc.
S2：Using the variable sequence for model parameter optimization, and setting model hyper-parameters; the hyper-parameters include the length L of the FIR and the width m of the model hidden layer(2)；
S3: constructing a model structure according to the set hyper-parameters, and initializing model parameters; wherein, the model structure is constructed as shown in FIG. 2, the first layer of the model includes a parameter matrix W(1)∈RL×mThe second layer of the model contains a parameter matrix
And a parameter vector
The output layer of the model contains parameter vectors
And parameter b(2)E is R; model parameters are initialized by the following formula:
wherein lLRepresenting a full one vector of dimension L,/L+1And
respectively represent dimensions L +1 and m(2)All one vectors of (a);
and
representing parameters contained in a second layer of the model, and respectively representing the connection weight and the threshold value of the second layer;
a representation matrix W(2)The ith row and the jth column of (1); l represents the length of the FIR; m represents the dimension of the auxiliary variable, m(2)Representing the width of the model hidden layer; the superscript T denotes the transpose of the matrix or vector, W(1)The representation is a model first layer parameter, representing the weight coefficients of the FIR,
means 1 line m(2)The set of real transverse quantities of a column,
means m rows m(2)A set of real matrices of columns;
s4: training an optimization model; as shown in fig. 3, the step of training the optimization model includes:
s41: inputting a sampling sequence U, y of an auxiliary variable and a main variable in the sulfur recovery process, simultaneously setting iteration times and training step length of parameter optimization, recording N and m as the length of the input sequence and the dimension of the auxiliary variable respectively, and making N equal to N-L + 1; wherein, inputting auxiliary variables of the sulfur recovery process, and calculating a constant matrix C belonging to RL×mAnd D ∈ RL×L×m；
Wherein the calculation constant matrix is obtained by the following formula:
wherein U represents a sample sequence of auxiliary variables; c and D are constant matrixes and constant tensors and are used for recording the mean value and the variance of the auxiliary variable U on each time segment of each dimension respectively; c:,iIs the ith column vector of the matrix C, represents the mean sequence of the ith auxiliary variable,
representing the three-dimensional tensor Dth1Line t2The element corresponding to the ith block of the column represents the ith auxiliary variablet1Time value and t2Covariance statistics of time values; n represents the length of the input sequence; "+" denotes a discrete finite convolution operation; u shape(n:1),i＝[un,i,un-1,i,…,u1,i]，uj,iIs the element corresponding to the jth row and ith column of the matrix U, where t is1、t2And i denotes the index of the matrix or tensor, R, for the row and column in which the element liesL×L×mSet of real tensor, R, referring to L blocks, L rows and m columnsL×mRefers to a real number matrix set of L rows and m columns;
s42: calculating forward propagation of the model to obtain a sequence, wherein as shown in fig. 4, the step of calculating forward propagation of the model to obtain the sequence includes:
s421: the FIR parameter is used to filter the auxiliary variable, and it should be noted that the following formula is used for filtering the auxiliary variable by the FIR parameter:
wherein H(1)For the output result of the first layer of the model (i.e. FIR layer), W(1)∈RL×mIs a parameter matrix of the FIR layer;
represents the output sequence H(1)Column i, U:,iAnd
also representing the matrices U and W, respectively(1)Of the ith column vector, RL×mRefers to a real number matrix set of L rows and m columns;
s422: performing layer normalization operation, wherein the layer normalization operation is realized by the following formula:
wherein the content of the first and second substances,
and
respectively represent column vectors
The mean and variance of; d:,:,iRepresenting a matrix corresponding to the ith block of the three-dimensional tensor Dith;
is a vector
The result after normalization; lNRepresenting a full row vector of dimension N; c:,i TRepresents a column vector C:,iTransposing; w:,i (1)A representation matrix W(1)The ith column vector of (1); lNRepresenting a full row vector of dimension N; ξ represents a constant parameter, a small positive constant, and is set to prevent the denominator of equation (6) from approaching 0;
s423: calculating an output sequence of the hidden layer, wherein the output sequence of the hidden layer is realized by using the following formula:
wherein "g" represents a Sigmoid function;
and
for the second layer parameter of the model, respectively representing the connection weight and the connection weight of the Sigmoid layerA threshold value;
and
respectively representing the input quantity and the output quantity of the Sigmoid function; b(2)Representing parameters contained in the second layer of the model;
s424: and (3) calculating the average value of the second layer output sequence, and normalizing the sequence, as shown in formula (8):
wherein the content of the first and second substances,
representing the second layer output sequence H of the model(2)The mean vector of (2);
is sequence H(2)The centering result of (a); lNRepresenting a full row vector of dimension N; lN TRepresenting a full one vector lNTransposing; n represents a dimension;
s43: and performing model back propagation calculation to obtain derivatives of the first and second layer parameters with respect to the cost function J, wherein as shown in fig. 5, the step of performing the model back propagation calculation to obtain the derivatives of the first and second layer parameters with respect to the cost function J includes:
s431: and solving the optimal value of the output layer parameter, wherein the optimal value of the output layer parameter is solved based on the least square principle, and the formula based on the least square principle is as follows:
where λ is a non-negative regular term and can be set to 5 by default, and equation (10) is a defined cost function, m of which(j)Representing the width of the jth layer of the model; i is an identity matrix; mu.syIs a leading variable; y is formed by RN×1，
The centering result is the sequence y;
and b(3)E, taking R as an output layer parameter of the model, and respectively representing the connection weight and the threshold of the output layer;
is sequence H(2)The centering result of (a);
representing the second layer output sequence H of the model(2)The mean vector of (2);
an ith column vector representing a weight matrix in the jth layer of the model;
s432: calculating the gradient of the first and second layer parameters layer by layer, as shown in formulas (11) to (14):
wherein the content of the first and second substances,
the expression dimension is m(2)A full row vector of;
s44: optimizing the model parameters according to an Adam algorithm;
s45: judging whether the iteration times are reached, if so, updating the output layer parameters of the model by using an equation (9), and determining mu by using an equation (5)(1)And σ(1)Ending the parameter optimization; if not, returning to S32;
s46: updating the output layer parameters by using the formula (9);
s5: model prediction, wherein, as shown in fig. 6, the model prediction comprises the steps of:
s51: inputting the dominant variable of the test set sample into the model;
s52: according to the model forward propagation, a prediction sequence of a dominant variable is calculated, specifically, firstly, FIR filtering is carried out on a new auxiliary variable by using an equation (4), and therefore useful characteristics H are extracted(1)Then, for the characteristic sequence H(1)Normalization is performed, as shown in formula (6), then forward propagation is performed through formula (7), an output sequence of the Sigmoid layer is calculated, and finally, a predicted value of the dominant variable is output through formula (15), wherein formula (15) is as follows:
wherein the content of the first and second substances,
representing the sequence of predicted values of the dominant variable y.
The model of the invention considers the time sequence information of the sulfur recovery process, and can effectively avoid the over-fitting phenomenon, thereby ensuring the prediction precision and further ensuring the normal operation of closed-loop control by means of a soft measurer before the sensor is aged or damaged.
Example 2
Referring to fig. 9 and 10, in the present embodiment, during sulfur recovery, a monitoring staff king uses a solid metal oxide semiconductor sensor to perform real-time measurement and collection of concentrations of tail GAS H2S and SO2, and simultaneously uses a GAS flow sensor to perform collection of MEA _ GAS flow, AIR _ MEA AIR flow, AIR _ MEA _2 secondary AIR flow, SWS zone GAS flow and SWS zone AIR flow, and tail GAS H is obtained by using a GAS flow sensor2S and SO2The concentration, the MEA _ GAS GAS flow, the AIR _ MEA AIR flow, the AIR _ MEA _2 secondary AIR flow, the SWS area GAS flow and the SWS area AIR flow are sampled at the sampling interval of 1 minute, 10081 sampling data are collected, and the collected data upload the measured values of the variables at each moment to an upper computer by using a 485 bus; wherein, tail gas H in the process of selecting sulfur recovery is selected2S and SO2The concentration is used as a leading variable, the MEA _ GAS GAS flow, the AIR _ MEA AIR flow, the AIR _ MEA _2 secondary AIR flow, the SWS area GAS flow and the SWS area AIR flow are selected as auxiliary variables, the first 7000 samples are selected from 10081 sampling data to be used as training samples, and the rest 3081 samples are used for testing.
The specific implementation mode is as follows: setting the width L of convolution kernel to 50 and the number m of Sigmoid layer nodes(2)Xi is 10 when 20 is greater-6Setting the regular term coefficient as 5, and establishing two independent models to respectively realize the real-time estimation of the concentrations of the hydrogen sulfide and the sulfur dioxide; firstly, a training sample is sent into a model for parameter optimization, and 1000 iterations are performed in total; and after the training is finished, sending the rest test samples into the model, and predicting to obtain the value of the dominant variable in the rest 3081 minutes.
To verify the effectiveness of the present invention, a Gaussian Process Regression (GPR) provided by Matlab and the present method were used to model and compare the datasets and the Root Mean Square Error (RMSE) was used to measure the predicted effect of the model.
The modeling result of the GPR is shown in FIG. 9, the modeling result of the method is shown in FIG. 10, and it can be understood from the graph that the GPR and the method have similar performance in a training set, while the prediction effect of the method is far superior to that of the traditional GPR in a test sample set, which shows that the GPR has a serious overfitting phenomenon in modeling, but the method is relatively simple in model structure, and timing sequence information of a sulfur recovery process is considered, so that the overfitting phenomenon can be effectively avoided, and the prediction accuracy is ensured.
As can be seen from fig. 9 and 10, after the process runs for 7000 minutes, the sulfide sensor cannot be normally used due to corrosion of the acid gas, at this time, the prediction accuracy of the conventional soft measurement model is rapidly reduced, and the change of the dominant variable cannot be tracked, but the soft measurement model of the present invention is hardly affected, and still can ensure better prediction accuracy, tables 1 and 2 respectively show the prediction performance indexes of the present invention for the concentrations of hydrogen sulfide and sulfur dioxide, including the root mean square error, the average absolute deviation, the average relative error, and the correlation coefficient between the predicted value and the true value.
Table 1 model prediction performance index for hydrogen sulfide concentration
Table 2 model prediction performance index for sulfur dioxide concentration
It is important to note that the construction and arrangement of the present application as shown in the various exemplary embodiments is illustrative only. Although only a few embodiments have been described in detail in this disclosure, those skilled in the art who review this disclosure will readily appreciate that many modifications are possible (e.g., variations in sizes, dimensions, structures, shapes and proportions of the various elements, values of parameters (e.g., temperatures, pressures, etc.), mounting arrangements, use of materials, colors, orientations, etc.) without materially departing from the novel teachings and advantages of the subject matter recited in this application. For example, elements shown as integrally formed may be constructed of multiple parts or elements, the position of elements may be reversed or otherwise varied, and the nature or number of discrete elements or positions may be altered or varied. Accordingly, all such modifications are intended to be included within the scope of this invention. The order or sequence of any process or method steps may be varied or re-sequenced according to alternative embodiments. In the claims, any means-plus-function clause is intended to cover the structures described herein as performing the recited function and not only structural equivalents but also equivalent structures. Other substitutions, modifications, changes and omissions may be made in the design, operating conditions and arrangement of the exemplary embodiments without departing from the scope of the present inventions. Therefore, the present invention is not limited to a particular embodiment, but extends to various modifications that nevertheless fall within the scope of the appended claims.
Moreover, in an effort to provide a concise description of the exemplary embodiments, all features of an actual implementation may not be described (i.e., those unrelated to the presently contemplated best mode of carrying out the invention, or those unrelated to enabling the invention).
It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions may be made. Such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure, without undue experimentation.
It should be noted that the above-mentioned embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, which should be covered by the claims of the present invention.
Claims (9)
1. A dynamic sulfur recovery soft measurement modeling method based on a parameterized FIR model is characterized in that: comprises the steps of (a) preparing a mixture of a plurality of raw materials,
in the sulfur recovery process, a sensor is adopted and the tail gas is measured and collected in real time at a fixed sampling frequency to obtain a variable sequence of the sulfur recovery process;
using the variable sequence for model parameter optimization, and setting model hyper-parameters;
constructing a model structure according to the set hyper-parameters, and initializing model parameters;
training an optimization model;
model prediction;
the variable sequence is divided into an auxiliary variable and a main variable;
the model parameter initialization is by the following formula:
wherein lLRepresenting a full one vector of dimension L,/L+1And
respectively represent dimensions L +1 and m(2)All one vectors of (a);
and
representing parameters contained in a second layer of the model, and respectively representing the connection weight and the threshold value of the second layer;
a representation matrix W(2)The ith row and the jth column of (1); l represents the length of the FIR; m represents the dimension of the auxiliary variable, m(2)Display moduleThe width of the type hidden layer; the superscript T denotes the transpose of the matrix or vector, W(1)The representation is a model first layer parameter, representing the weight coefficients of the FIR.
2. The parameterized FIR model-based dynamic sulfur recovery soft measurement modeling method of claim 1, characterized in that: the sensor is divided into a solid metal oxide semiconductor sensor and a gas flow sensor, and the solid metal oxide semiconductor sensor is used for detecting tail gas H2S and SO2The concentration is collected in real time measurements and the GAS flow sensors collect the MEA _ GAS flow, AIR _ MEA AIR flow, AIR _ MEA _2 secondary AIR flow, SWS zone GAS flow, and SWS zone AIR flow.
3. The parameterized FIR model-based dynamic sulfur recovery soft measurement modeling method of claim 2, characterized in that: the step of training the optimization model comprises:
inputting a sampling sequence of an auxiliary variable and a main variable in the sulfur recovery process, and simultaneously setting iteration times and training step length of parameter optimization;
calculating forward propagation of the model to obtain a sequence;
calculating the back propagation of the model to obtain the derivatives of the first and second layer parameters with respect to the cost function J;
optimizing the model parameters according to an Adam algorithm;
judging whether the iteration times are reached;
and updating the parameters of the output layer.
4. The parameterized FIR model based dynamic sulfur recovery soft measurement modeling method of claim 3, characterized in that: inputting sulfur recovery process auxiliary variables, and calculating a constant matrix C belonging to RL×mAnd D ∈ RL×L×m；
Wherein the calculation constant matrix is obtained by the following formula:
wherein U represents a sample sequence of auxiliary variables; c represents a constant matrix; d denotes a constant tensor; c:,iThe ith column vector of the matrix C represents the mean value sequence of the ith auxiliary variable;
and
respectively represent the t-th matrix C1Rows ith and tth2The element corresponding to line i;
representing the three-dimensional tensor Dth1Line t2The element corresponding to the ith block of the column represents the ith auxiliary variable t1Time value and t2Covariance statistics of time values;
and
respectively representing the ith auxiliary scalar at the t-t1And τ -t2The value of the variable at the moment; n represents the length of the input sequence; u shape(n:1),i＝[Un,i,Un-1,i,…,U1,i]，Uj,iThe element corresponding to the jth row and ith column of the matrix U; n represents a dimension; lNRepresenting a full row vector of dimension N; "+" denotes a discrete finite convolution operation.
5. The parameterized FIR model based dynamic sulfur recovery soft measurement modeling method according to claim 4, characterized in that: the step of calculating the forward propagation of the model to obtain the sequence comprises the following steps:
filtering the auxiliary variable by using the FIR parameter;
carrying out layer normalization operation;
calculating an output sequence of the hidden layer;
and solving the average value of the second layer output sequence and normalizing the sequence.
6. The parameterized FIR model based dynamic sulfur recovery soft measurement modeling method according to claim 5, characterized in that: the FIR parameter filters the auxiliary variable by adopting the following formula:
wherein H(1)As output results of the first layer of the model, W(1)∈RL×mIs a parameter matrix of the FIR layer;
represents the output sequence H(1)Column i, U:,iAnd
respectively representing matrices U and W(1)The ith column vector of (1).
7. The parameterized FIR model based dynamic sulfur recovery soft measurement modeling method of claim 6, characterized in that: the layer normalization operation is performed according to the following formula:
wherein the content of the first and second substances,
and
respectively represent column vectors
The mean and variance of; d:,:,iRepresenting a matrix corresponding to the ith block of the three-dimensional tensor Dith;
vector representation
The result after normalization; lNRepresenting a full row vector of dimension N; c:,i TRepresents a column vector C:,iTransposing; w:,i (1)A representation matrix W(1)The ith column vector of (1); lNRepresenting a full row vector of dimension N; ξ denotes a constant parameter.
8. The parameterized FIR model-based dynamic sulfur recovery soft measurement modeling method of claim 7, wherein: the step of calculating the back propagation of the model to obtain the derivatives of the first and second layer parameters with respect to the cost function J comprises the following steps:
obtaining the optimal value of the output layer parameter;
and calculating the gradient of the first layer parameter and the second layer parameter layer by layer.
9. The parameterized FIR model-based dynamic sulfur recovery soft measurement modeling method of claim 8, wherein: the model predicts:
inputting the dominant variable of the test set sample into the model;
and calculating a prediction sequence of the dominant variable according to the forward propagation of the model.
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