Dynamic design method for test signal of rectifying tower based on power spectrum

Abstract

The invention discloses a dynamic design method of a rectifying tower test signal based on a power spectrum, and belongs to the field of industrial processes. The method comprises the steps of firstly designing a mean value and a standard deviation of an output signal based on a variance characteristic of a power spectrum, further designing a probability constraint of the output signal, and fully considering a dynamic characteristic of a test signal from a frequency domain angle; then, the amplitude of the rectifying tower test signal is dynamically designed based on probability constraint, the problem that the test process is too conservative due to traditional steady-state design is solved, the test signal can more sufficiently excite a test object within the constraint range, and meanwhile the effect of multi-channel parallel test is achieved. According to the invention, the amplitude of the test signal can be effectively enhanced within the constraint range, the time required by the test is reduced, the quality of the test data is improved, and the power spectrum-based dynamic design method for the test signal of the rectifying tower is realized.

Description

Technical Field

[0001] The invention belongs to the field of industrial processes, and in particular, relates to a dynamic design method for a distillation tower test signal based on a power spectrum. Background Art

[0002] In industrial processes, model predictive control algorithms are often used to reasonably control the production process of distillation towers, and the model of the distillation tower needs to be obtained using the system identification method. In the system identification experiment, the design of the test signal determines the quality of the entire test experiment and directly affects the quality of the input and output data of the distillation tower 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 high-quality system identification experiments and lay a solid foundation for the subsequent development of model predictive control algorithms.

[0003] Traditional test signal design methods are often designed based on the steady-state model of the system. However, since the average switching time of the test signal is short, the output of the system will not fully reach the steady state during the test. As a result, 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 subsequent model identification.

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

[0005] The purpose of the present invention is to overcome the defects in the prior art and provide a method for dynamic design of distillation tower test signals based on power spectrum. The present invention introduces the concept of power spectrum, designs the probability constraints 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 stimulate the test object within the constraint range and improve the quality of the test data. The present invention uses the power spectrum to dynamically optimize the amplitude of the distillation tower test signal, which can more fully stimulate the test object, thereby improving the quality of the test data and the model accuracy of the subsequent system identification.

[0006] The specific technical solutions adopted by the present invention are as follows:

[0007] In a first aspect, the present invention provides a method for dynamic design of distillation tower test signals based on power spectrum, which is 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 constraints of the output channel signal;

[0009] S2. Use the negative number of the cumulative multiplication of the test signal amplitude as the minimization penalty function, so that the input channel test signal satisfies the input constraint, the output channel signal satisfies 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.

[0010] Preferably, in S1, the mean 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.

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

[0012] 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.

[0013] Preferably, the standard deviation of the output channel signal is the square root of the variance of the output channel signal, and the variance of the output channel signal is obtained by analyzing from the frequency domain perspective, as follows:

[0014] 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.

[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 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.

[0016] Preferably, in S1, the probability that the output channel signal satisfies the upper and lower limit constraints is , 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 Standard Deviation The signal quantity satisfies the upper and lower limit constraints of the output channel signal.

[0017] Preferably, in S2, the input channel test signal enumerates all possible signal combinations as follows:

[0018]

[0019] 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, is the number of input channels, For nth u The amplitude of the test signal of each input channel; represents a diagonal matrix; S is a possible combination of input channel test signals.

[0020] Preferably, the possible input channel test signal combination S satisfies:

[0021] .

[0022] In a second aspect, the present invention provides a computer program product, including a computer program / instruction, which, when executed by a processor, can implement the power spectrum-based dynamic design method for a distillation tower test signal as described in any one of the first aspects.

[0023] In a third aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the power spectrum-based dynamic design method for a distillation tower test signal as described in any one of the first aspects is implemented.

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

[0025] The memory is used to store computer programs;

[0026] The processor is used to implement the power spectrum-based dynamic design method for distillation tower test signals as described in any one of the first aspects 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. However, due to the short average switching time of the test signal, the output of the system will not fully reach the steady state during the test, resulting in the problem of conservative 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 considers the dynamic characteristics of the system, and then dynamically designs the amplitude of the distillation tower test signal based on the probability constraint. The amplitude of the test signal thus optimized is significantly higher than the amplitude optimized by the steady-state design. The test signal can more fully excite the test object within the constraint range, thereby improving the quality of the test data.

[0029] (2) In order to solve the problem that multi-channel testing is difficult to implement in existing industrial process system identification experiments, the present invention takes the form of multi-channel amplitude multiplication as the optimization target and dynamically designs the multi-channel amplitude size of the distillation tower test signal based on probability constraints. Compared with the traditional single-channel test scheme, it can effectively save the time of the test experiment and improve the accuracy of model identification. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The purpose, features and advantages of the present invention can be further understood by describing the preferred embodiments of the present invention in conjunction with the accompanying drawings. The present invention is described in more detail below with reference to the accompanying drawings of the present invention. However, the present invention can also be implemented in many different forms, so it should not be considered that it is limited to the embodiments listed in the specification. On the contrary, such embodiments are provided 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 A dynamic design method for distillation column test signals based on power spectrum.

[0032] Figure 2 This is the experimental result of the distillation tower simulation test process. DETAILED DESCRIPTION

[0033] The present invention is further described and illustrated below in conjunction with the accompanying drawings and specific embodiments. The technical features of each embodiment of the present invention can be combined accordingly without conflicting with each other.

[0034] The input of the distillation tower system is reflux flow control and sensitive plate temperature control, and the output is reflux ratio and tower top temperature. A GBN signal (generalized binary noise signal) is used as a test signal, and the amplitude of the test signal is designed by the method of the present invention. Before the method of the present invention is adopted, there should be an a priori model for the distillation tower system for testing the method of the present invention, but the accuracy of the a priori model is low, and the accuracy of the model can be improved by the method of the present invention.

[0035] The present invention provides a method for dynamic design of distillation tower test signals based on power spectrum. The method first designs the mean and standard deviation of output channel signals based on the variance characteristics of the power spectrum, and further designs the probability constraints of the output channel test signals, and fully considers the dynamic characteristics of the test signals from the frequency domain perspective; then, the amplitude of the distillation tower test signal is dynamically designed based on the probability constraints, overcoming the problem of overly conservative testing process caused by traditional steady-state design, so that the test signal can more fully stimulate the test object within the constraint range, and at the same time achieve the effect of multi-channel parallel testing. Compared with the traditional single-channel testing scheme, it can effectively save the time of the test experiment and obtain high-quality test data.

[0036] like Figure 1 As 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 constraints of the output channel signal;

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

[0039] As a preferred embodiment of the present invention, in the above step S1, the mean and standard deviation of the output channel signal are designed based on the variance characteristic of the power spectrum in the following specific operations:

[0040] The mean value y of the output channel signal avg It is obtained by calculating the steady-state prediction model, that is, assuming 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, which is specifically expressed as the following formula:

[0041]

[0042] Among them, y0 is the last item of the initial prediction value, u avg is the mean value 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 from the frequency domain analysis, 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 and 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 frequency, the composite trapezoidal formula is used to discretize the above process and integrate it, and the continuous power spectrum function is divided into n sampling frequencies. Finally, the standard deviation of the required output channel signal can be designed. 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 jth output channel signal, n is the number of frequency samples; is the frequency and satisfies ; is the power spectrum of the jth output channel including the amplitude coefficients.

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

[0047]

[0048] in, is the modulus of the transfer function frequency response of the i-th input channel to the j-th output channel, The power spectrum of the input channel test signal; is the power spectrum of the GBN signal of the i-th output channel. When the time domain information of the GBN signal is known, its power spectrum is known; is the frequency response of the transfer function, For nth u The transfer function frequency response of the jth output channel corresponding to the jth input channel is: is the transfer function frequency response of the 1st input channel corresponding to the jth output channel.

[0049] As a preferred embodiment of the present invention, the mean value y of the output signal avg and standard deviation After the above process is completed, the probability that the output signal meets the upper and lower limit constraints is , and conforms to the standard normal distribution, then the probability constraint can be designed based on the confidence interval equivalent to the output signal mean y avg Nearby positive and negative Standard Deviation The signal quantity satisfies the upper and lower limit constraints of the output signal, which is specifically expressed as follows:

[0050]

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

[0052] As a preferred embodiment of the present invention, in the above step S2, the amplitude of the distillation tower test signal is dynamically designed based on probability constraints as follows:

[0053] The design optimization proposition is to solve the amplitude of the optimal test signal. The goal is to minimize the negative number of the cumulative multiplication of the test signal amplitude. The input signal satisfies the input constraint, the output signal satisfies the probability constraint in S1, and the input signal enumerates all possible signal combinations. The proposition is replaced by matrix S. The amplitude of the test signal is non-negative. The dynamic optimization proposition of the distillation tower test signal amplitude based on probability constraints is as follows:

[0054]

[0055] Among them, J is the penalty function, represents the minimization penalty function, st(·) represents the constraint of the proposition, and a i is the amplitude of the test signal of the i-th input channel, is the number of input channels, For nth u The amplitude of the input channel test signal; the input channel test signal ,u i The actual value of the test signal of each input channel of the distillation tower; the average value of the test signal of the input channel ,uavg,i is the mean of the test signals 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 The upper limit of the constraint for the test signal of each input channel of the distillation tower; the mean value of the output channel signal ,y avg,i is the mean value of each output channel signal of the distillation tower; the lower limit of the output channel signal ,y min,i is the lower limit of the output channel signal of the distillation tower; the upper limit of the output channel signal ,y max,i is the upper limit of the output channel signal of the distillation tower; the standard deviation of the output channel signal , Represents the standard deviation of the output channel signals of the distillation tower; represents a diagonal matrix; S is a possible combination of input signals that satisfies:

[0056] ,

[0057] and is the solution to this optimization problem.

[0058] The above method is applied to a specific embodiment below to demonstrate its technical effect.

[0059] In this embodiment, taking a 2*2 distillation tower model as an example, the optimization strategy of the 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 as follows:

[0061] The negative number of the cumulative multiplication of the test signal amplitude is used as the minimization penalty function, the input channel test signal is required to meet the input constraint, and the output channel signal meets the output constraint. The steady-state prediction model is used to establish an equality constraint between the input and output, and then the amplitude of the distillation tower test signal is designed in a steady state.

[0062] Table 1 Comparison of results

[0063]

[0064] In the above table, a i is the amplitude of the test signal of the i-th input channel. The experimental results are as follows: Figure 2As shown. y1, y2 are output channel signals, the dotted lines are upper and lower limit constraints, u1, u2 are input channel test signals, and u set1 、u set2 is the set sequence, the horizontal axis is the sampling time, and the vertical axis is the signal size. It can be seen from the figure that the output channel signal expands the test range as much as possible within the constraint range, can more fully stimulate the test object, the input channel signal can effectively track the set sequence, and achieve the effect of multi-channel parallel testing, greatly reducing the time required for the test experiment, and 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] 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 for distillation tower test signals based on power spectrum.

[0066] The above-described embodiment is only a preferred solution of the present invention, but it is not intended to limit the present invention. A person skilled in the relevant technical field may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, any technical solution obtained by equivalent replacement or equivalent transformation falls 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. Use the negative number of the cumulative multiplication of the test signal amplitude as the minimization penalty function, so that the input channel test signal satisfies the input constraint, the output channel signal satisfies 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.

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 , 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 Standard Deviation The signal quantity 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, is the number of input channels, For nth u The amplitude of the test signal of each input channel; 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 power spectrum-based dynamic design method for a distillation tower test signal 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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