A dynamic design method for the test signal of a distillation column based on the power spectrum

Abstract

The present invention discloses a dynamic design method for a rectification column test signal based on power spectrum, belonging to the field of industrial processes. The method first designs the mean and standard deviation of the output signal based on the variance characteristics of the power spectrum, and further designs the probability constraint of the output signal, fully considering the dynamic characteristics of the test signal from the frequency domain perspective; then dynamically designs the amplitude of the rectification column test signal based on the probability constraint, overcomes the problem of excessive conservatism in the test process caused by traditional steady-state design, enables the test signal to more fully stimulate the test object within the constraint range, and at the same time achieves the effect of multi-channel parallel testing. The present invention can effectively enhance the amplitude of the test signal within the constraint range, reduce the time required for testing, improve the quality of test data, and realize a dynamic design method for a rectification column test signal based on power spectrum.

Description

Technical Field

[0001] The present invention belongs to the field of industrial processes. In particular, it relates to a dynamic design method for test signals of a distillation column based on power spectrum. Background Art

[0002] In industrial processes, the model predictive control algorithm is often used to reasonably control the production process of a distillation column. The model of the distillation column needs to be obtained by the method of system identification. In the system identification experiment, the design of the test signal determines the quality of the entire test experiment, directly affecting the quality of the input and output data of the distillation column system. High-quality test data can effectively improve the accuracy of the identified model. Therefore, it is necessary to reasonably design the amplitude of the test signal to achieve a high-quality system identification experiment and lay a solid foundation for the subsequent development of the model predictive control algorithm.

[0003] In traditional test signal design methods, the design is often based on the steady-state model of the system. Due to the short average switching time of the test signal, the output of the system during the test does not reach the steady state sufficiently. Therefore, there is a problem that the signal excitation during the test is relatively conservative, which will lead to a decrease in the quality of the test data and affect the accuracy of the subsequent model identification.

[0004] Therefore, there is an urgent need to provide a new dynamic design method for test signals of a distillation column. Summary of the Invention

[0005] The purpose of the present invention is to overcome the defects in the prior art and provide a dynamic design method for test signals of a distillation column based on power spectrum. The present invention introduces the concept of power spectrum, designs the probability constraint of the output signal, and fully considers the dynamic characteristics of the test signal from the frequency domain perspective. Compared with the steady-state design, the test signal designed by the present invention can more fully excite the test object within the constraint range and improve the quality of the test data. The present invention uses power spectrum to dynamically optimize the amplitude of the test signal of the distillation column, which can more fully excite the test object, thereby improving the quality of the test data and the accuracy of the subsequent system identification model.

[0006] The specific technical solution adopted by the present invention is as follows:

[0007] In the first aspect, the present invention provides a dynamic design method for test signals of a distillation column based on power spectrum, specifically as follows:

[0008] S1. Design the mean and standard deviation of the output channel signal based on the variance characteristics of the power spectrum, and further design the probability constraint of the output channel signal;

[0009] S2. Use the negative product of the test signal amplitudes as the minimization penalty function, and make the test signals of the input channels satisfy the input constraints and the signals of the output channels satisfy the probability constraints described in S1. Also, enumerate all possible signal combinations of the test signals of the input channels, and then dynamically design the amplitudes of the test signals for the distillation column.

[0010] Preferably, in S1, the mean value of the output channel signal is calculated through the steady-state model, and the standard deviation of the output channel signal is obtained through the variance.

[0011] Preferably, the mean value of the output channel signal is obtained specifically through the following method:

[0012] Assume the mean value u of the test signal of the input channel avg is known, then the mean value y of the output channel signal avg is equivalent to the last term of the prediction initial value of the previous moment's prediction model plus the product of the model steady-state gain and the difference between the mean value of the test signal of the input channel and the actual value of the test signal of the input channel at the previous moment.

[0013] Preferably, the standard deviation of the output channel signal is the square root of the variance of the output channel signal. The variance of the output channel signal is obtained from the frequency-domain analysis, specifically as follows:

[0014] Use the generalized binary noise signal with amplitude a as the test signal of the input channel. Then, multiply the sum of the squares of the modulus of the frequency response of the transfer function between the input channel and a selected output channel, the power spectrum of the generalized binary noise signal, and the square of its amplitude. The power spectrum of a single output signal is equivalent to the sum of the products of each input channel after the above multiplication;

[0015] The variance of the output channel signal is equivalent to the value of the inverse Fourier transform of the output signal power spectrum when the time constant is 0, and is also equivalent to the product of the integral of the output signal power spectrum from -π to π and 1 / 2π. Since the power spectrum of the output channel signal is a function of continuous frequencies, the composite trapezoidal formula is used to discretize and integrate the above process. The continuous power spectrum function is divided into n sampling frequencies, and finally the standard deviation of the required output channel signal is obtained.

[0016] Preferably, in S1, the probability that the output channel signal satisfies the upper and lower limit constraints is , and it conforms to the standard normal distribution. Then, the probability constraint is equivalently designed according to the confidence interval as the signal amount within plus or minus avg near the mean value y of the output channel signal standard deviations satisfies the upper and lower limit constraints of the output channel signal.

[0017] Preferably, in S2, the enumeration of all possible signal combinations of the test signals of the input channels is specifically as follows:

[0018]

[0019] Among them, the mean value of the input channel test signal , u avg,i is the mean value of the test signals of each input channel of the rectification column; a i is the amplitude of the test signal of the i-th input channel, is the number of input channels, is the n u -th amplitude of the test signal of the input channel; represents a diagonal matrix; S is a combination of test signals of input channels that may occur.

[0020] Preferably, the combination S of test signals of input channels that may occur satisfies:

[0021] .

[0022] In a second aspect, the present invention provides a computer program product, including a computer program / instructions, which, when executed by a processor, can implement the dynamic design method of the rectification column test signal based on the power spectrum as described in any item of the first aspect.

[0023] In a third aspect, the present invention provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the dynamic design method of the rectification column test signal based on the power spectrum as described in any item of the first aspect is implemented.

[0024] In a fourth aspect, the present invention provides a computer electronic device, including a memory and a processor;

[0025] The memory is used to store a computer program;

[0026] The processor is used to implement the dynamic design method of the rectification column test signal based on the power spectrum as described in any item of the first aspect when executing the computer program.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] (1)The test experiments of existing industrial processes are often designed based on the steady-state model of the system. Since the average switching time of the test signal is short, the output of the system during the test will not reach the steady state sufficiently, resulting in a more conservative problem of signal excitation during the test. To address this problem, the present invention designs the probability constraint of the output signal based on the power spectrum, fully considering the dynamic characteristics of the system, and then dynamically designs the amplitude of the test signal for the distillation column based on the probability constraint. The amplitude of the test signal optimized in this way is significantly higher than that optimized by the steady-state design. The test signal can more fully excite the test object within the constraint range, improving the quality of the test data.

[0029] (2)To address the problem that multi-channel testing is difficult to achieve in the system identification experiment of existing industrial processes, the present invention takes the form of multi-channel amplitude multiplication as the optimization objective and dynamically designs the multi-channel amplitude of the test signal for the distillation column based on the probability constraint. Compared with the traditional single-channel testing scheme, it can effectively save the time of the test experiment and improve the accuracy of model identification. Description of the Drawings

[0030] By describing the preferred embodiments of the present invention in combination with the following drawings, the purpose, features, and advantages of the present invention can be further understood. The present invention will be described in more detail with reference to the drawings of the present invention. However, the present invention can be implemented in many different forms, so it should not be considered limited to the embodiments listed in the specification. On the contrary, providing such embodiments is to illustrate the implementation and completeness of the present invention and to describe the specific implementation process of the present invention to those skilled in the art.

[0031] Figure 1 It is a dynamic design method for the test signal of the distillation column based on the power spectrum.

[0032] Figure 2 It is the experimental effect of the simulation test process of the distillation column. Detailed Embodiments

[0033] The present invention will be further elaborated and described below in combination with the drawings and specific embodiments. The technical features of each embodiment of the present invention can be combined accordingly without conflict.

[0034] The inputs of the distillation column system are reflux flow control and sensitive plate temperature control, and the outputs are reflux ratio and top temperature. The GBN signal (Generalized Binary Noise Signal) is used as the test signal, and the present invention method is used to design the amplitude of the test signal. Before using the present invention method, there should be a prior model in the distillation column system for the test of the present invention method. However, the accuracy of this prior model is low, and the accuracy of this model can be improved by the present invention method.

[0035] The present invention provides a dynamic design method for the test signal of a distillation column based on the power spectrum. This method first designs the mean and standard deviation of the output channel signal based on the variance characteristics of the power spectrum, and further designs the probability constraint of the output channel test signal, fully considering the dynamic characteristics of the test signal from the frequency domain perspective. Then, it dynamically designs the amplitude of the test signal of the distillation column based on the probability constraint, overcomes the problem of excessive conservatism in the test process caused by traditional steady-state design, enables the test signal to more fully stimulate the test object within the constraint range, and at the same time achieves the effect of multi-channel parallel testing. Compared with the traditional single-channel test scheme, it can effectively save the time of the test experiment and obtain high-quality test data.

[0036] As Figure 1 shown, the method of the present invention specifically includes the following two steps:

[0037] S1. Design the mean and standard deviation of the output channel signal based on the variance characteristics of the power spectrum, and further design the probability constraint of the output channel signal;

[0038] S2. Dynamically design the amplitude of the test signal of the distillation column based on the probability constraint.

[0039] As a relatively preferred embodiment of the present invention, in the above step S1, the operation of designing the mean and standard deviation of the output channel signal based on the variance characteristics of the power spectrum is as follows:

[0040] The mean y of the output channel signal avg is calculated through the steady-state prediction model, that is, assuming that the mean u of the input channel test signal avg is known, then the mean y of the output channel signal avg is equivalent to the last term of the prediction initial value of the prediction model at the previous moment plus the steady-state gain of the model multiplied by the difference between the mean of the input channel test signal and the actual value of the input channel test signal at the previous moment, specifically expressed as the following formula:

[0041]

[0042] where y0 is the last term of the prediction initial value, u avg is the mean of the input channel test signal, u0 is the actual value of the input channel test signal at the previous moment, and K is the steady-state gain of the prediction model.

[0043] The standard deviation of the output channel test signal can be obtained based on the variance characteristics of the power spectrum, that is, the standard deviation of the output channel test signal is the square root of the variance of the output channel signal, and the variance of the output channel signal can be obtained by analyzing from the frequency domain perspective, that is, the variance of the output channel signal is equivalent to the value of the inverse Fourier transform of the power spectrum of the output channel signal when the time constant is 0, and is also equivalent to the product of the integral of the power spectrum of the output channel signal from -π to π and 1 / 2π. Since the power spectrum of the output channel signal is a function of continuous frequencies, the composite trapezoidal formula is used to discretize and integrate the above process. The continuous power spectrum function is divided into n sampling frequencies, and finally the standard deviation of the required output channel signal can be designed and obtained. The specific formula is as follows:

[0044]

[0045] where j = 1,...,n y , n y is the number of output channel signals, is the standard deviation of the j-th output channel signal, is the variance of the j-th output channel signal, and n is the number of frequency samplings; is the frequency and satisfies ; is the power spectrum of the j-th output channel including the amplitude coefficient.

[0046] Specifically, the test signal of the output channel is generated by the combined action of multiple GBN signals with amplitudes as the input channel test signals on the prediction model. Since the GBN signal is a generalized binary random noise, there is no correlation between different GBN signals and no cross-spectrum. Furthermore, it can be designed to multiply the power spectrum of each GBN signal itself by the square of its amplitude and then by the modulus of the transfer function frequency response of the corresponding input channel and the j-th output channel. After performing the above operations on each input channel and then accumulating them, the power spectrum of the j-th output channel can be obtained, which is specifically expressed as the following formula:

[0047]

[0048] where, is the modulus of the transfer function frequency response of the i-th input channel corresponding to the j-th output channel, is the power spectrum of the input channel test signal; is the power spectrum of the GBN signal of the i-th output channel, and its power spectrum is known when the time domain information of the GBN signal is known; is the frequency response of the transfer function, is the transfer function frequency response of the n u -th input channel corresponding to the j-th output channel, is the frequency response of the transfer function corresponding to the j-th output channel for the first input channel.

[0049] As a preferred embodiment of the present invention, the mean value y of the output signal avg and the standard deviation After being calculated by the above process, the probability that the output signal satisfies the upper and lower limit constraints is , and it conforms to the standard normal distribution. Then the probability constraint can be equivalently designed according to the confidence interval as the signal amount of plus or minus avg near the mean value y of the output signal standard deviations satisfies the upper and lower limit constraints of the output signal, which is specifically expressed as follows:

[0050]

[0051] Wherein, is the critical value of the standard normal distribution, and , is a certain probability value, is the cumulative distribution function of the standard normal random variable; the standard deviation of the output signal , y min is the lower limit of the output signal, y max is the upper limit of the output signal.

[0052] As a preferred embodiment of the present invention, in the above step S2, the specific operation of dynamically designing the amplitude of the distillation column test signal based on the probability constraint is as follows:

[0053] Design an optimization proposition to solve the amplitude of the optimal test signal. Its goal is to minimize the negative product of the test signal amplitudes. The input signal satisfies the input constraints, the output signal satisfies the probability constraint in S1, and the input signal enumerates all possible signal combinations. It is replaced by the matrix S in the proposition. The amplitude of the test signal is non-negative. Then the dynamic optimization proposition of the distillation column test signal amplitude based on the probability constraint is as follows:

[0054]

[0055] Wherein, J is the penalty function, represents minimizing the penalty function, s.t.(·) represents the constraint of the proposition, a i is the amplitude of the test signal for the i-th input channel, is the number of input channels, is the amplitude of the test signal for the n u -th input channel; the test signal of the input channel , u i is the actual value of the test signal for each input channel of the distillation column; the mean value of the test signal of the input channel , uavg,i is the mean value of the test signals of each input channel of the distillation column; the lower bound of the constraint of the test signal of the input channel , u min,i is the lower bound of the constraint of the test signals of each input channel of the distillation column; the upper bound of the constraint of the test signal of the input channel , u max,i is the upper bound of the constraint of the test signals of each input channel of the distillation column; the mean value of the output channel signal , y avg,i is the mean value of the signals of each output channel of the distillation column; the lower bound of the constraint of the output channel signal , y min,i is the lower bound of the constraint of the signals of each output channel of the distillation column; the upper bound of the constraint of the output channel signal , y max,i is the upper bound of the constraint of the signals of each output channel of the distillation column; the standard deviation of the output channel signal , represents the standard deviation of the signals of each output channel of the distillation column; represents a diagonal matrix; S is a possible combination of input signals and satisfies:

[0056] ,

[0057] and are the solutions to this optimization problem.

[0058] Next, the above method will be applied to a specific embodiment to demonstrate its technical effects.

[0059] In this embodiment, taking a 2*2 distillation column model as an example, the optimization strategies of traditional steady-state design and the optimization strategy of the present invention are respectively implemented, and the results are compared, as shown in Table 1.

[0060] Among them, the optimization strategy method of traditional steady-state design is specifically as follows:

[0061] Taking the negative of the product of the amplitudes of the test signals as the minimization penalty function, making the test signals of the input channels satisfy the input constraints, the signals of the output channels satisfy the output constraints, and establishing an equality constraint between the input and output with a steady-state prediction model, and then steadily designing the amplitude of the test signals of the distillation column.

[0062] Table 1 Result comparison

[0063]

[0064] In the above table, a i is the amplitude of the test signal of the i-th input channel, and the experimental effect is as Figure 2As shown. y1 and y2 are output channel signals, the dashed lines are upper and lower limit constraints, u1 and u2 are input channel test signals, u set1 and u set2 is the set sequence, the abscissa is the sampling time, and the ordinate is the signal magnitude. It can be seen from the figure that the output channel signals expand the test range as much as possible within the constraint range, can more fully stimulate the test object, the input channel signals can effectively track the set sequence, and achieve the effect of multi-channel parallel testing, greatly reducing the time required for the test experiment. Moreover, compared with the traditional method, the test amplitude of the method of the present invention is significantly enhanced, which can further improve the quality of the test data.

[0065] Thus, it can be seen that the method adopted by the present invention can effectively solve the problem that the traditional steady-state design test process is too conservative, while reducing the time required for the test experiment, improving the quality of the test data, and realizing a dynamic design method of the test signal for the distillation column based on the power spectrum.

[0066] The above-described embodiments are only a preferred solution of the present invention, but it is not intended to limit the present invention. Those of ordinary skill in the relevant technical field can still make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, all technical solutions obtained by adopting the equivalent replacement or equivalent transformation method fall within the protection scope of the present invention.

Claims

1. A dynamic design method for distillation tower test signal based on power spectrum, characterized in that: The details are as follows: S1. Design the mean and standard deviation of the output channel signal based on the variance characteristics of the power spectrum, and further design the probability constraints of the output channel signal; S2, using the negative number of the cumulative multiplication of the test signal amplitude as the minimization penalty function, making the input channel test signal satisfy the input constraint, the output channel signal satisfy the probability constraint described in S1, and the input channel test signal enumerates all possible signal combinations, and then dynamically designs the amplitude of the distillation tower test signal; The input constraints are in min Oh, oh. max In the formula, the input channel test signal u i is the actual value of the test signal of each input channel of the distillation tower; the lower limit of the input channel test signal u min,i The lower limit of the test signal of each input channel of the distillation tower; the upper limit of the test signal of the input channel u max,i Test the upper limit of the signal constraints for each input channel of the distillation column.

2. The method for dynamic design of distillation tower test signals based on power spectrum according to claim 1, characterized in that: In S1, the mean value of the output channel signal is obtained by calculating the steady-state model, and the standard deviation of the output channel signal is obtained by the variance.

3. The method for dynamic design of distillation tower test signals based on power spectrum according to claim 2, characterized in that: The mean value of the output channel signal is specifically obtained by the following method: Assume that the mean value u of the input channel test signal avg Known, the mean value y of the output channel signal avg It is equivalent to the last item of the predicted initial value of the prediction model at the previous moment plus the model steady-state gain multiplied by the difference between the mean value of the input channel test signal and the actual value of the input channel test signal at the previous moment.

4. The method for dynamic design of distillation tower test signals based on power spectrum according to claim 2, characterized in that: The standard deviation of the output channel signal is the square root of the variance of the output channel signal. The variance of the output channel signal is obtained from the frequency domain analysis, as follows: A generalized binary noise signal with amplitude a is used as the input channel test signal, and then the square of the modulus of the transfer function frequency response of the input channel and a selected output channel and the power spectrum of the generalized binary noise signal and the square of its amplitude are multiplied. Then the power spectrum of a single output signal is equivalent to the cumulative sum of each input channel after the above products. The variance of the output channel signal is equivalent to the value of the inverse Fourier transform of the output signal power spectrum when the time constant is 0, and is also equivalent to the product of the integral of the output signal power spectrum from -π to π and 1 / 2π. Since the power spectrum of the output channel signal is a function of continuous frequency, the composite trapezoidal formula is used to discretize and integrate the above process, and the continuous power spectrum function is divided into n sampling frequencies, and finally the standard deviation of the required output channel signal is obtained.

5. The method for dynamic design of distillation tower test signals based on power spectrum according to claim 2, characterized in that: In S1, the probability that the output channel signal satisfies the upper and lower limit constraints is α, and conforms to the standard normal distribution. Then the probability constraint is designed according to the confidence interval equivalent to the output channel signal mean y avg Nearby positive and negative z α / 2 The signal quantity with a standard deviation σ satisfies the upper and lower limit constraints of the output channel signal.

6. A method for dynamic design of distillation tower test signals based on power spectrum according to claim 5, characterized in that: In S2, the input channel test signal enumerates all possible signal combinations as follows: Among them, the mean value of the input channel test signal u avg,i is the average value of the test signal of each input channel of the distillation tower; a i is the amplitude of the test signal of the i-th input channel, n u is the number of input channels, For nth u The amplitude of the input channel test signal; diag(·) represents a diagonal matrix; S is a possible combination of input channel test signals.

7. The method for dynamic design of distillation tower test signals based on power spectrum according to claim 6, characterized in that: The possible input channel test signal combination S satisfies:

8. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instruction is executed by a processor, the power spectrum-based dynamic design method for distillation tower test signals as described in any one of claims 1 to 7 can be implemented.

9. A computer-readable storage medium, characterized in that: The storage medium stores a computer program, and when the computer program is executed by a processor, the method for dynamic design of distillation tower test signals based on power spectrum as described in any one of claims 1 to 7 is implemented.

10. A computer electronic device, characterized in that: including memory and processor; The memory is used to store computer programs; The processor is used to implement the power spectrum-based dynamic design method for distillation tower test signals as described in any one of claims 1 to 7 when executing the computer program.

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