CN102645315B - Automatic, fast and accurate detection method for air resistance characteristics of large heat exchanger - Google Patents

Abstract

The invention discloses an automatic, rapid and accurate detection method for the air resistance characteristic of a large heat exchanger. The existing measurement and control system for the air resistance characteristics of plate-fin heat exchangers is difficult to realize automatic and rapid measurement. The present invention first carries out data mining according to the historical test data, adopts the support vector machine to establish the general relationship between the design parameters of the heat exchanger and the initial frequency, and obtains the control characteristics of the heat exchanger channels through the automatic identification of the control characteristic parameters of different heat exchanger channels , use the optimal performance index to set the PID parameters of the automatic controller, and then use the incremental PID controller to control the converted standard value of the air volume of the air duct to the set standard air volume, and obtain its value by detecting the air resistance value at this time air resistance characteristics. The invention can realize the automatic and fast measurement of the gas resistance characteristic of the large heat exchanger, has high testing precision, and effectively improves the production efficiency.

Description

An automatic, rapid and accurate detection method for air resistance characteristics of large heat exchangers

technical field

The invention belongs to the technical field of control and relates to data modeling and process control in the field of industrial process control. It mainly involves a method for measuring the air resistance characteristics of large-scale plate-fin heat exchangers, which automatically and quickly controls the air volume of the heat exchanger to the set air volume value after the transformation, and then obtains the air resistance of the heat exchanger through detection. property value.

Background technique

The air resistance characteristic is an important indicator to characterize the flow performance of large heat exchangers, and it is also one of the important indicators that large plate-fin heat exchanger products must be tested before leaving the factory. It mainly includes two aspects: one is for a certain heat exchanger channel, under the conditions of standard temperature, standard pressure and standard flow, the pressure loss at both ends of the heat exchanger channel; the other is the heat exchanger channel in this case friction factor. Due to different test results under different temperature, pressure and other conditions, there is a lack of comparability. Therefore, it is stipulated that the standard condition is under a standard atmospheric pressure and the standard zero degree Celsius is the standard condition. The air volume measured at this time is the standard air volume, and the air volume measured under other pressures and temperatures needs to be converted into the standard air volume. In the past, in the measurement process, the orifice flowmeter was generally used to measure the air resistance parameters of the heat exchanger under a certain air volume, and then converted to obtain the air resistance characteristics of the heat exchanger under standard conditions. The above methods have obvious disadvantages. One is that the measurement accuracy of the orifice flowmeter is relatively poor. In addition, the air volume control adopts the method of manually controlling the valve, which cannot accurately control the air volume after the transformation. The third is to use orifice plate measurement. And manual control is not energy-saving, inaccurate, and the amount of subsequent manual calculations is large. Due to the long test time of each heat exchanger, the work efficiency is relatively low.

The frequency converter is used to control the air volume of the fan, and the nozzle measurement system can solve the energy-saving problem of the system. The accuracy of the air volume measurement by the nozzle is much higher than that of the orifice flowmeter. Since the current working condition cannot be guaranteed to be in the standard working condition during the test, it is necessary to convert the temperature and pressure of the heat exchanger according to the gas state equation. The conversion method is: ,here and stands for standard temperature and pressure, is the measured wind volume, and are the measured pressure and temperature, is the converted standard measured air volume. For the sake of accuracy, during the heat exchanger channel performance test, the air volume is quickly controlled to the converted standard measured air volume, that is, the measured air volume is required to be converted into the measured standard air volume, and then the measured standard air volume is controlled to be equal to the set standard Air volume. Considering the test efficiency and energy-saving requirements, the measurement device adopts frequency conversion technology to adjust the air volume.

Another feature of the test of different channels of the heat exchanger is that the test is intermittent: that is, after testing a channel, the air volume of the air duct of the measuring device is required to be zero before a new channel is connected to the measuring device. Due to the different models and types of each heat exchanger, how to determine the initial frequency of the fan during the test, and how to use an appropriate control method to quickly and stably control the air volume corresponding to the standard working condition according to the characteristics of the system under test It has an important influence on the measurement accuracy and rapidity of the heat exchanger. Due to the hysteresis of the measurement system, the great difference in the load characteristics of different channels, and the nonlinear characteristics of the frequency conversion signal, it is difficult for the system to achieve automatic and fast measurement. Therefore, it is necessary to study a method that can realize automatic and rapid measurement and control of air volume in this case, so as to meet the industrial requirements of the air resistance characteristic test of plate-fin heat exchanger.

Contents of the invention

The purpose of the present invention is to provide a method for automatically and quickly measuring the air resistance characteristics of different heat exchangers with different channel characteristics. In this method, firstly, data mining is carried out based on historical test data, and the general relationship between the design parameters of the heat exchanger and the initial frequency is established by using the support vector machine, and then the heat exchanger is obtained through automatic identification of the control characteristic parameters of different heat exchanger channels. The control characteristics of the channel, use the optimal performance index to set the PID parameters of the automatic controller, and then use the incremental PID controller to control the converted standard value of the air volume of the air duct to the set standard air volume, by detecting the air resistance at this time value to obtain its air resistance characteristics.

Concrete steps of the present invention are:

Step (1) Collect the design parameters and detection parameters of different types of plate-fin heat exchangers, and establish a real-time database containing the design parameters and detection parameters of the heat exchanger; the heat exchanger design parameters include the channel name, design Standard air volume, design air resistance, friction factor, detection parameters include actual air resistance of heat exchanger, ambient temperature, air pressure and fan frequency. On this basis, based on the historical test data, the relationship model between the design standard air volume, design air resistance, ambient temperature, actual air resistance, and actual fan frequency is established by using the support vector machine integrated modeling method with strong generalization ability. Predict the required frequency value of the fan to achieve the set standard air volume under different heat exchanger channel setting standard air volume and design air resistance . The specific modeling method is as follows:

The input parameters and output parameters for modeling samples can be expressed as ,in Indicates the first Set as a parameter vector of input data, including design standard air volume, design air resistance and ambient temperature, Indicates the first Set as output parameter vector, including actual air resistance and actual fan frequency, is the sample size.

For the support vector machine algorithm, the kernel function is selected as the radial basis function:

is the radial basis function, is the mapping function, Indicates the first group as a parameter vector of input data, , is the kernel parameter of the radial basis function, and the objective function sought is: , is the predicted value of the actual air resistance and fan frequency output by the model, is the weight coefficient vector, is the intercept, in order to calculate and value. Introduce relaxation factor and , and allow the fitting error to be , and Values can be passed in constraints:

, conditionally minimizes:

get, where is the structural risk minimization function, constant is the penalty coefficient, and as a parameter variable. The minimization problem is a convex quadratic programming problem, and the Lagrangian function is introduced:

     

in: ≥0, ≥0, is the Lagrangian multiplier.

At a saddle point, the Lagrange function its about The smallest point of The maximum point, then the above minimization problem is transformed into the maximization problem of its dual problem. Lagrange function At the saddle point is about At a minimum, we get:

                    

The dual function of the Lagrangian function can be obtained :

at this time,

According to the Kuhn-Tucker (KKT) conditional theorem, the following formula holds at the saddle point:

             

It can be seen from the above formula, , and will not be non-zero at the same time, we can get:

  

It can be obtained from the above formula .

According to the above support vector machine algorithm, the steps of the support vector machine integrated modeling method are as follows:

a. The original training data initialization weight is , is the number of weight updates, when initializing the weight , set the number of iterations .

b. Call the above support vector machine algorithm to model the training samples and obtain a model ,calculate The squared value of the average forecast error for : .

c. Update the original training data weights: .

d. According to the new weight distribution of the original training data, sampling is performed in the original training set, and the sampling conditions are: , Sampling thresholds for the set weights generate a training set for sub-support vector machines.

e. Repeat steps b~d to obtain a new model and a new sub-training set until iterations are completed.

f. will get Sub-support vector machine models are integrated, and the model weights are: , the final integrated model obtained is: , For the obtained support vector machine ensemble model.

Step (2) According to the design standard air volume, design air resistance and ambient temperature conditions of a channel of the actual heat exchanger, use the model established in step (1) to predict that a channel of the heat exchanger reaches the initial value of the fan frequency under the set standard air volume , due to the test conditions and there is no strong mechanism correlation between the input and output, the fan at the initial frequency Although the air volume under the condition is not much different from the actual set standard air volume requirements, it still cannot meet the requirements. It needs to be corrected again and the actual air volume should be controlled to the set standard air volume through automatic control.

Step (3) According to the initial value of the frequency obtained in step (2) , adjust the fan frequency from 0 to 80% of , when the frequency reaches 80% and run stably for 10-20s, adjust the frequency of the variable fan to 100% , and stabilized for 10-20s, the measured standard air volume at this time is recorded as , the fan frequency reaches 80% of the air volume and the measured standard air volume when it runs stably for 10-20s is recorded as . And at frequency from 80% to 100% And in the process of stabilizing for 10-20s, record the measured standard air volume, measured air resistance and fan frequency of the heat exchanger channel at a period of 0.5-1s. Then, change the frequency from 80% to 100% And stabilize the measured standard air volume and fan frequency recorded during the 10-20s process to subtract and , to get the air volume change value, denoted as , and the frequency change value, denoted as ,in and represent the record's first Air volume change and frequency change values.

Step (4) According to the characteristics of the pipeline gas flow control model, the transfer function between frequency and air volume is established. The transfer function of the air volume control system can be regarded as a first-order inertia plus delay link, so the transfer function between the frequency and the standard air volume can be set as ,in represent the open-loop magnification, time constant and delay time, respectively, is plural. Obtained according to step (3) ,Will Assign positive initial values respectively, and pass the transfer function Calculate the control quantity at the sampling point output under action , then end with As the goal, the least squares algorithm is used to fit the three parameters in the transfer function , to get the specific transfer function of a certain channel of the heat exchanger.

Step (5) After the transfer function of the heat exchanger channel control characteristics is established in step (4), in order to ensure that the air volume is adjusted to the preset standard air volume quickly and stably, the parameters of the PID are adjusted. Taking the IATE integral performance as the optimal index, taking the parameters in the PID controller , , As a variable, take PID+ As the open-loop transfer function, with the closed-loop transfer function as the constraint equation, with , , All positive values are variable constraints, and the nonlinear optimization solution technology is used to optimize the solution to obtain the optimal PID controller parameters , , value, where , , represent the proportional, integral and derivative parameters, respectively.

Step (6) Obtain the initial frequency according to step (2) and the frequency obtained in step (3) , calculate the approximate linear relationship parameters between air volume and frequency, and determine the correction value of the initial frequency , adjust the fan frequency to , and stable Second. According to the similarity principle, the frequency There is an approximate relationship with the air volume as . and That is, the linear relationship parameter that needs to be obtained. The frequency obtained in step (3) will be as well as The lower air volume, into the above relational formula to obtain the parameters and . in getting and after, according to relationship, order In order to set the standard air volume, the fan frequency prediction correction value can be obtained under the set standard air volume .

Step (7) Set the fan frequency at Frequency point, wait for the frequency to reach the set value and stabilize seconds later. Then the incremental PID controller is used to control the measured air volume of the heat exchanger channel at the set standard air volume, and the air resistance characteristics of the heat exchanger channel under the set standard air volume are obtained. The output form of PID is:

;

Here the three parameters of the incremental PID controller , , For the three parameters obtained in step (5). Indicates the sampling period, Represents the error between the set value and the feedback value of the corresponding steps, , , Respectively represent the current frequency value, the frequency change value and the next frequency value. Through incremental PID control, the measured air volume value can be automatically controlled at the set standard air volume value, and the control accuracy is within 0.5%. At this time, the air resistance characteristic obtained by measurement is the air resistance characteristic under the set standard air volume. Through the comparison between the measured air resistance and the designed air resistance, the performance index of the air resistance characteristic of the heat exchanger can be obtained.

Beneficial effects of the present invention: the method not only completely replaces the previous method of manually detecting the air resistance characteristic of the heat exchanger, but also has the characteristics of automatic detection, automatic calculation and high test accuracy. The method has excellent automation and rapidity, can adapt to different loads and air volume requirements, and can greatly speed up the number of heat exchanger test batches while improving test accuracy and reducing manual workload.

Detailed ways

An automatic, rapid and accurate detection method for the air resistance characteristics of a large heat exchanger, the specific implementation adopts the following steps:

Step (1) Collect the design parameters and detection parameters of different types of plate-fin heat exchangers, and establish a real-time database containing the design parameters and detection parameters of the heat exchanger; the heat exchanger design parameters include the channel name, design Standard air volume, design air resistance, friction factor, detection parameters include actual air resistance of heat exchanger, ambient temperature, air pressure and fan frequency. On this basis, based on the historical test data, the relationship model between the design standard air volume, design air resistance, ambient temperature, actual air resistance, and actual fan frequency is established by using the support vector machine integrated modeling method with strong generalization ability. Predict the required frequency value of the fan to achieve the set standard air volume under different heat exchanger channel setting standard air volume and design air resistance . The specific modeling method is as follows:

The input parameters and output parameters for modeling samples can be expressed as ,in Indicates the first Set as a parameter vector of input data, including design standard air volume, design air resistance and ambient temperature, Indicates the first Set as output parameter vector, including actual air resistance and actual fan frequency, is the sample size.

For the support vector machine algorithm, the kernel function is selected as the radial basis function:

is the radial basis function, is the mapping function, Indicates the first group as a parameter vector of input data, , is the kernel parameter of the radial basis function, and the objective function sought is: , is the predicted value of the actual air resistance and fan frequency output by the model, is the weight coefficient vector, is the intercept, in order to calculate and value. Introduce relaxation factor and , and allow the fitting error to be , and Values can be passed in constraints:

, conditionally minimizes:

get, where is the structural risk minimization function, constant is the penalty coefficient, and as a parameter variable. The minimization problem is a convex quadratic programming problem, and the Lagrangian function is introduced:

     

in: ≥0, ≥0, is the Lagrangian multiplier.

At a saddle point, the Lagrange function its about The smallest point of The maximum point, then the above minimization problem is transformed into the maximization problem of its dual problem. Lagrange function At the saddle point is about At a minimum, we get:

                    

The dual function of the Lagrangian function can be obtained :

at this time,

According to the Kuhn-Tucker (KKT) conditional theorem, the following formula holds at the saddle point:

             

It can be seen from the above formula, , and will not be non-zero at the same time, we can get:

  

It can be obtained from the above formula .

According to the above support vector machine algorithm, the steps of the support vector machine integrated modeling method are as follows:

a. The original training data initialization weight is , is the number of weight updates, when initializing the weight , set the number of iterations .

b. Call the above support vector machine algorithm to model the training samples and obtain a model ,calculate The squared value of the average forecast error for : .

c. Update the original training data weights: .

d. According to the new weight distribution of the original training data, sampling is performed in the original training set, and the sampling conditions are: , Sampling thresholds for the set weights generate a training set for sub-support vector machines.

e. Repeat steps b~d to obtain a new model and a new sub-training set until iterations are completed.

f. will get Sub-support vector machine models are integrated, and the model weights are: , the final integrated model obtained is: , For the obtained support vector machine ensemble model.

Step (2) According to the design standard air volume, design air resistance and ambient temperature conditions of a channel of the actual heat exchanger, use the model established in step (1) to predict that a channel of the heat exchanger reaches the initial value of the fan frequency under the set standard air volume , due to the test conditions and there is no strong mechanism correlation between the input and output, the fan at the initial frequency Although there is little difference from the actual set standard air volume requirements, it still cannot meet the requirements. It needs to be corrected again and the actual air volume should be controlled to the set standard air volume through automatic control.

Step (3) According to the initial value of the frequency obtained in step (2) , adjust the fan frequency from 0 to 80% of , when the frequency reaches 80% of the frequency and after running stably for 10-20s, adjust the inverter frequency to 100% , and stabilized for 10-20s, the standard measured air volume at this time is recorded as , the inverter frequency reaches 80% of the standard measured air volume when it runs stably for 10-20s is recorded as . And at frequency from 80% to 100% And in the process of stabilizing for 10-20s, record the standard measured air volume, measured air resistance and fan frequency after conversion of the heat exchanger channel with a period of 0.5-1s. Then, change the frequency from 80% to 100% And the standard measured air volume and fan frequency recorded in the process of stabilizing for 10-20s are respectively subtracted and , to get the air volume change value, denoted as , and the frequency change value, denoted as ,in and represent the record's first Air volume change and frequency change values.

Step (4) According to the characteristics of the pipeline gas flow control model, the transfer function between frequency and air volume is established. The transfer function of the air volume control system can be regarded as a first-order inertia plus delay link, so the transfer function between the frequency and the standard air volume can be set as ,in represent the open-loop magnification, time constant and delay time, respectively, is plural. Obtained according to step (3) ,Will Assign positive initial values respectively, and pass the transfer function Calculate the control quantity at the sampling point output under action , then end with As the goal, the least squares algorithm is used to fit the three parameters in the transfer function , to get the specific transfer function of a certain channel of the heat exchanger.

Step (5) After the transfer function of the heat exchanger channel control characteristics is established in step (4), in order to ensure that the air volume is adjusted to the preset standard air volume quickly and stably, the parameters of the PID are adjusted. Taking the IATE integral performance as the optimal index, taking the parameters in the PID controller , , As a variable, take PID+ As the open-loop transfer function, with the closed-loop transfer function as the constraint equation, with , , All positive values are variable constraints, and the nonlinear optimization solution technology is used to optimize the solution to obtain the optimal PID controller parameters , , value, where , , represent the proportional, integral and derivative parameters, respectively.

Step (6) Obtain the initial frequency according to step (2) and the frequency obtained in step (3) , calculate the approximate linear relationship parameters between air volume and frequency, and determine the correction value of the initial frequency , adjust the fan frequency to , and stable Second. According to the similarity principle, the frequency There is an approximate relationship with the air volume as . and That is, the linear relationship parameter that needs to be obtained. The frequency obtained in step (3) will be as well as The lower air volume, into the above relational formula to obtain the parameters and . in getting and after, according to relationship, order In order to set the standard air volume, the fan frequency prediction correction value can be obtained under the set standard air volume .

Step (7) Set the fan frequency at Frequency point, wait for the frequency to reach the set value and stabilize seconds later. Then the incremental PID controller is used to control the measured air volume of the heat exchanger channel at the set standard air volume, and the air resistance characteristics of the heat exchanger channel under the set standard air volume are obtained. The output form of PID is:

; Here the three parameters of the incremental PID controller , , For the three parameters obtained in step (5). Indicates the sampling period, Represents the error between the set value and the feedback value of the corresponding steps, , , Respectively represent the current frequency value, the frequency change value and the next frequency value. Through incremental PID control, the measured air volume value can be automatically controlled at the set standard air volume value, and the control accuracy is within 0.5%. At this time, the air resistance characteristic obtained by measurement is the air resistance characteristic under the set standard air volume. Through the comparison between the measured air resistance and the designed air resistance, the performance index of the air resistance characteristic of the heat exchanger can be obtained.

Claims (1)

1. A method for automatic, rapid and accurate detection of air resistance characteristics of large heat exchangers, characterized in that the steps of the method include: Step (1) collect design parameters and detection parameters of different types of heat exchangers, and establish a real-time database containing design parameters and detection parameters of heat exchangers; The heat exchanger design parameters include the channel name of the heat exchanger, design standard air volume, design air resistance and friction factor; the detection parameters include the actual air resistance of the heat exchanger, ambient temperature, air pressure and fan frequency; On this basis, based on the historical test data, the support vector machine integrated modeling method with strong generalization ability is used to establish the relationship between the design standard air volume, design air resistance, ambient temperature, actual air resistance, and actual fan frequency, so as to predict Under the standard air volume and design air resistance of different heat exchanger channels, the frequency value f ₀ required by the fan to achieve the set standard air volume; the specific modeling method is as follows: The input parameters and output parameters used to model the samples are expressed as Among them, x _i represents the parameter vector of group i as input data, including design standard air volume, design air resistance and ambient temperature, y _i represents the parameter vector of group i as output, including actual air resistance and actual fan frequency, and N is the sample quantity; For the support vector machine algorithm, the kernel function is selected as the radial basis function: $<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; (</span>\frac{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span>$ K(x _i , x _j ) is the radial basis function, φ(x) is the mapping function, x _j represents the parameter vector of the jth group as input data, j=1,..., N, σ is the radial basis function kernel parameters, let the objective function to be sought be: f(x _i )=w·φ(x _i )+b, f(x _i ) is the predicted value of the actual air resistance and fan frequency output by the model, and w is the weight coefficient vector , b is the intercept, in order to calculate w and b values; introduce relaxation factor ξ _i ≥ 0 and And allow fit errors for ε, w and b values by passing in constraints: $\left\{\begin{array}{c}{\mathrm{the\; y}}_i-w\&CenterDot;\mathrm{\&phi;}\left(x_i\right)-b\&le;\mathrm{\&epsiv;}+{\mathrm{\&xi;}}_i\\ w\&CenterDot;\mathrm{\&phi;}\left(x_i\right)+b-{\mathrm{the\; y}}_i\&le;\mathrm{\&epsiv;}+{\mathrm{\&xi;}}_i^{*}\\ {\mathrm{\&xi;}}_i\&Greater\; Equal;0\\ {\mathrm{\&xi;}}_i^{*}\&Greater\; Equal;0\end{array}\right.i=1,\&Center\; Dot;\&CenterDot;\&Center\; Dot;,N,$ condition, minimize: $\mathrm{<span\; class="notranslate">\; min</span>}\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; c</span>}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}^{<span\; class="notranslate">\; *</span>}$ where R(w, ξ, ξ ^* ) is the structural risk minimization function, the constant c>0 is the penalty coefficient, ξ and ξ ^* are parameter variables; the minimization problem is a convex quadratic programming problem, and the Lager Langerian function: $\begin{array}{c}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; a</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; \&gamma;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; \&CenterDot;</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; c</span>}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span>\\ <span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; )</span>\end{array}$ in: is the Lagrangian multiplier; At a saddle point, the Lagrange function L is about The smallest point of At the maximum point, the above minimization problem is transformed into the maximization problem of its dual problem; the Lagrangian function L at the saddle point is about At a minimum, we get: $\left\{\begin{array}{c}\frac{<span\; class="notranslate">\; \&PartialD;</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; w</span>}}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&Right\; Arrow;</span>\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\\ \frac{<span\; class="notranslate">\; \&PartialD;</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; b</span>}}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&Right\; Arrow;</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \frac{<span\; class="notranslate">\; \&PartialD;</span>}{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&Right\; Arrow;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ \frac{<span\; class="notranslate">\; \&PartialD;</span>}{<span\; class="notranslate">\; \&PartialD;</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; \&Right\; Arrow;</span>\mathrm{<span\; class="notranslate">\; c</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.$ The dual function of the Lagrangian function can be obtained at this time, $\begin{array}{c}\mathrm{<span\; class="notranslate">\; w</span>}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; N</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; b</span>}\end{array}$ According to the Kuhn-Tucker conditional theorem, the following formula holds at the saddle point: $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; N</span>}\right.$ It can be seen from the above formula, α _i and will not be non-zero at the same time, we can get: $\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}{\mathrm{<span\; class="notranslate">\; \&gamma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\end{array}\right.\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&CenterDot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; \&Center\; Dot;</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; N</span>}$ b can be obtained from the above formula; According to the above support vector machine algorithm, the steps of the support vector machine integrated modeling method are as follows: a. The original training data initialization weight is jj is the number of weight updates, jj=1 when initializing the weight, and set the number of iterations k; b. Call the above support vector machine algorithm to model the training samples, obtain a model M _jj , and calculate the square value of the average prediction error of M _jj : c. Update the original training data weights: d. According to the new weight distribution of the original training data, sampling is performed in the original training set, and the sampling conditions are: β is the set weight sampling threshold to generate a training set for sub-support vector machines; e. Repeat steps b~d to obtain a new model M _jj+1 and a new sub-training set until k iterations are completed; f. Integrate the k sub-support vector machine models obtained, and the model weights are: The final integrated model obtained is: M _final is the obtained support vector machine ensemble model; Step (2) According to the design standard air volume, design air resistance and ambient temperature conditions of a certain channel of the heat exchanger, use the model established in step (1) to predict the initial value f of the fan frequency under the set standard air volume for a certain channel of the heat exchanger ₀ , due to the test conditions and the lack of strong mechanism correlation between input and output, although the fan’s initial frequency f ₀ is not much different from the actual set standard air volume requirements, it still cannot meet the requirements; it needs to be corrected again and automatically controlled The actual air volume is controlled to the set standard air volume; Step (3) According to the initial frequency value f ₀ obtained in step (2), adjust the fan frequency from 0 to 80% of f ₀ , which is recorded as f ₁ . When the frequency reaches 80% of f ₀ and runs stably for 10-20s , adjust the inverter frequency to 100% f ₀ , and stabilize it for 10-20s. At this time, the standard measured air volume is recorded as Q _w . The standard measured air volume when the inverter frequency reaches 80% of f ₀ and runs stably for 10-20s is Q _w1 ; while the frequency is from 80%f ₀ to 100%f ₀ and stabilized for 10-20s, record the standard measured air volume, measured air resistance and fan frequency after conversion of the heat exchanger channel with a cycle of 0.5-1s; then , subtracting Q _w1 and f ₁ from the measured air volume and fan frequency recorded during the frequency from 80% f ₀ to 100% f ₀ and stabilizing for 10-20 _s ; get the air volume change value, recorded as And the frequency change value, recorded as u=[u ₁ ,u ₂ ,...,u _cc ], where and u _cc represent the recorded cc-th wind volume change and frequency change value respectively; Step (4) According to the characteristics of the pipeline gas flow control model, the transfer function between the frequency and the air volume is established; the transfer function of the air volume control system is regarded as the first-order inertia plus delay link, so the transfer function between the frequency and the standard air volume can be set as Where K _z , T _t , τ represent the open-loop magnification, time constant and delay time respectively, and s is a complex number; according to u=[u1,u ₂ ,...,u _cc ] obtained in step (3), K _z , T _t , τ are given positive initial values respectively, and through the transfer function Calculate the output Q=(Q ₁ ,Q ₂ ,...,Q _cc ) under the action of the control variable u at the sampling point, and then use As the goal, the three parameters K _z , T _t , τ in the transfer function are fitted by the least squares algorithm, and the specific transfer function of a certain channel of the heat exchanger is obtained; Step (5) After the transfer function of the heat exchanger channel control characteristics is established in step (4), in order to ensure that the air volume is adjusted to the preset standard air volume quickly and stably, the parameters of the PID are adjusted; with the IATE integral performance as the optimal index, Take the parameters K _p , T _i , T _d in the PID controller as variables, and take As the open-loop transfer function, the closed-loop transfer function is used as the constraint equation, K _p , T _i , and T _d are all positive values as variable constraints, and the nonlinear optimization solution technology is used to optimize the solution to obtain the optimal PID controller parameter K _p , T _i , T _d values, where K _p , T _i , T _d represent proportional, integral and differential parameters respectively; Step (6) According to the initial frequency f ₀ obtained in step (2) and the frequency f ₁ obtained in step (3), calculate the approximate linear relationship parameter between the air volume and frequency, and determine the corrected value f′ ₀ of the initial frequency. The fan frequency is adjusted to f′ ₀ and stabilized for τ seconds; according to the similarity principle, there is an approximate relationship between the frequency f and the air volume Q _w as Q _w ≈ _{d 1} f+d ₂ ; d ₁ and d ₂ are the linear relationship parameters that need to be obtained ; The frequency f ₀ obtained in step (3) and the air volume under f ₁ are brought into the above relational formula to obtain parameters d ₁ and d ₂ ; after obtaining d ₁ and d ₂ , according to f=(Q _w -d ₂ ) The relationship between /d ₁ , let Q _w be the set standard air volume, and the fan frequency prediction correction value f′ ₀ under the set standard air volume can be obtained; Step (7) Set the fan frequency at f′ ₀ frequency point, wait for the frequency to reach the set value and stabilize for τ seconds; then use the incremental PID controller to control the measured air volume of the heat exchanger channel to the set standard air volume At the position, the air resistance characteristics of the heat exchanger channel under the set standard air volume are obtained; the output form of PID is: $\mathrm{<span\; class="notranslate">\; \&Delta;</span>}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; kk</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; kk</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; kk</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ]</span><span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; T</span>}}{{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; kk</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}\frac{\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; kk</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; kk</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; kk</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; ;</span>$ uu(kk+1)=uu(kk)+Δu _kk Here, the three parameters K _p , T _i , T _d of the incremental PID controller are the three parameters obtained in step (5); T represents the sampling period , e(kk), e(kk-1), e(kk-2) represent the error between the set value and the feedback value of the corresponding steps, uu(kk), Δuu(kk), uu(kk+1 ) represent the current frequency value, the frequency change value and the next frequency value respectively; through incremental PID control, the measured air volume value can be automatically controlled at the set standard air volume value, and the control accuracy is within 0.5%. The air resistance characteristic of the heat exchanger is the air resistance characteristic under the set standard air volume. Through the comparison between the measured air resistance and the designed air resistance, the performance index of the air resistance characteristic of the heat exchanger can be obtained.