Multi-stage air compressor air flow parameter iterative optimization method and system

Abstract

The present application relates to the technical field of air compressor control optimization, and specifically relates to a multi-stage air compressor airflow parameter iterative optimization method and system, which solves the technical problem that precise multi-stage airflow parameter optimization cannot be performed based on real-time physical state of equipment. The method comprises: presetting a sampling frequency to synchronously collect real-time state parameters of each stage of the multi-stage air compressor compression unit and the intermediate cooler; constructing a thermodynamic coupling model to online identify and update inter-stage flow resistance loss coefficients and heat exchange efficiency factors to form a constraint space reflecting the current actual physical state of the equipment; taking minimization of the overall machine specific power as the target, solving optimal pressure ratio distribution of each stage in the constraint space by using a super-linear convergence iterative method based on second-order gradient information of the target function; and converting the optimal pressure ratio distribution into exhaust pressure set values and rotation speed set values of each stage and outputting to an execution mechanism. The present application can always match the optimization constraint to the real physical state of the equipment, and realize energy saving and stable control in all working conditions.

Description

Technical Field

[0001] This invention relates to the field of air compressor control optimization technology, specifically to a method and system for iterative optimization of airflow parameters in a multi-stage air compressor. Background Technology

[0002] Compressed air is a widely used power source in industrial manufacturing systems, with important applications in energy and chemical engineering, aerospace, precision manufacturing, and large-scale public works. Multistage air compressors, characterized by high pressure ratio, interstage cooling, and variable efficiency, are core equipment for meeting the demand for high-flow, high-pressure industrial air.

[0003] In a multi-stage compression process, the gas state parameters after each stage of compression directly affect the work efficiency of that stage. They also constrain the intake and exhaust performance of subsequent stages through thermo-coupling links such as interstage coolers and interstage pipelines. Precise control of airflow parameters such as pressure, temperature, and flow rate inside a multi-stage air compressor is the core means to improve the overall energy efficiency of the machine and is also the key to preventing surge and overload when the equipment is operating under high load and variable conditions.

[0004] Traditional multi-stage air compressor control strategies rely on empirical models or static control curves formed from offline test data, using PID feedback to maintain exhaust pressure. This type of solution can only operate stably under steady-state conditions near the design point. When production load fluctuates drastically or environmental parameters change, the strong nonlinearity and hysteresis of the airflow field cause the empirical model to fail to capture the microscopic changes in the inter-stage flow regime in real time, and the system will continuously deviate from the optimal energy efficiency range.

[0005] Existing technologies primarily optimize control performance from the perspective of the power source. Some solutions improve motor response speed and operating efficiency through permanent magnet variable frequency air compressor motor parameter identification and control parameter self-tuning. However, these solutions do not conduct detailed modeling of the internal airflow thermodynamic processes of the air compressor. The core energy efficiency of a multi-stage air compressor depends on the thermodynamic circulation quality of the internal gas flow field, rather than simply mechanical speed or torque response. Improving motor control precision cannot solve the problems of internal energy loss and inter-stage blockage caused by airflow parameter mismatch.

[0006] Existing technologies utilize algorithms such as discrete particle swarm optimization (DPSO) to optimize the operation of clusters of multiple air compressors. While this approach can achieve a reasonable allocation of the plant's total power consumption, the optimization granularity is limited to the start-up, shutdown, and loading / unloading state transitions of individual units. Discrete optimization algorithms struggle to adapt to the high-dimensional, strongly coupled, nonlinear fluid dynamics characteristics of the continuous flow field within a single multi-stage air compressor. Each stage of the impeller, diffuser, and intercooler constitutes a dynamic subsystem, with cascading effects existing between airflow parameters. Furthermore, the lack of refined modeling and efficient iterative mechanisms for continuous airflow parameters within a single unit makes it impossible to meet the response accuracy and computational dimensionality requirements for transient operating condition transitions, hindering real-time optimization of airflow distribution within each stage of the flow path. Summary of the Invention

[0007] The purpose of this invention is to provide a method and system for iterative optimization of airflow parameters in multi-stage air compressors, which solves the technical problem that traditional multi-stage air compressor control strategies cannot achieve isomorphic mapping between physical degradation characteristics and mathematical optimization space due to static mapping or macroscopic scheduling schemes, resulting in limited energy efficiency optimization and safety protection effects.

[0008] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0009] Iterative optimization methods for airflow parameters in multi-stage air compressors include:

[0010] The system synchronously collects the intake pressure, intake temperature, exhaust pressure, exhaust temperature, and instantaneous mass flow rate of each compression unit of the multi-stage air compressor at a preset sampling frequency, as well as the inlet and outlet temperatures and flow rates of the cooling water in each stage of the intercooler, to form real-time status parameters.

[0011] A thermodynamic coupling model is constructed based on the real-time state parameters. The interstage flow resistance loss coefficient and heat transfer efficiency factor within the model are both identified and updated online based on the real-time state parameters. The interstage pressure transmission relationship is corrected by the online identified and updated interstage flow resistance loss coefficient, and the interstage temperature transmission relationship is corrected by the online identified and updated heat transfer efficiency factor. A constraint space that can reflect the current actual physical state of the equipment is constructed. The constraint space includes the allowable pressure ratio range and upper limit of the suction temperature of each stage determined by the corrected pressure transmission relationship and temperature transmission relationship, as well as the upper limit of the motor speed and surge boundary determined by the physical parameters of the equipment.

[0012] With minimizing the specific power of the whole machine as the objective function, an online optimization method based on the second-order gradient information of the objective function is used in the constrained space to determine the optimal pressure ratio allocation of each stage under the current working condition in real time. The optimal pressure ratio allocation obtained by the solution is converted into the exhaust pressure set value and speed set value of each stage and output to the actuator.

[0013] Furthermore, the interstage flow resistance loss coefficient is dynamically determined by combining the modified Fanning friction formula with the real-time calculated gas Reynolds number and pipeline roughness.

[0014] No. Level to No. Interstage flow resistance loss coefficient The following formula is used for calculation:

[0015]

[0016] in: For the first The exhaust port of the first stage compression unit to the first The equivalent piping length of the intake port of the primary compression unit, in units of ; The equivalent diameter of the pipeline is given in units of 1. ; The average density of the gas inside the pipeline, in units of ; The average gas velocity in the pipeline, in units of ; For the first The exhaust pressure of the compression unit is expressed in units of... ; The Darcy-Weisbach friction factor is updated in real time using the Colebrook formula based on the current Reynolds number and the equivalent roughness of the pipe wall. When solving this implicit equation online, the Newton iteration method is used, or the Swamee-Jain explicit formula is selected for approximate calculation to reduce the operator load.

[0017] Furthermore, the heat transfer efficiency factor is obtained through... The NTU method utilizes real-time measured cooling water temperature and flow rate, along with gas temperature and flow rate, to perform online identification. The identification process includes calculating the actual number of heat transfer units in the current heat exchanger, and then, based on the counter-current heat transfer relationship, reversibly solving for the heat transfer efficiency factor at the current moment. The nth... The heat transfer efficiency factor of the intercooler is .

[0018] Furthermore, the superlinear convergent iterative method based on the second-order gradient information of the objective function is the Newton-Raphson iterative method, and the iterative method uses the Armijo line search criterion to achieve adaptive step size control.

[0019] Update step size Armijo backtracking search is used to determine: starting from the initial step size Initially, if the condition is not met, the product is repeatedly multiplied by the attenuation factor. Continue until the maximum step size that satisfies the following conditions is selected:

[0020]

[0021] in: The objective function is... This is the current decision vector; Indicating the search direction; This is the transpose of the objective function with respect to the gradient of the decision vector; These are preset parameters, and their value range is [value range missing]. to .

[0022] Furthermore, the superlinear convergent iterative method based on the second-order gradient information of the objective function is a quasi-Newton method. This quasi-Newton method approximates the inverse of the Hessian matrix using the BFGS formula and employs the Armijo line search criterion to perform adaptive step size control; the BFGS formula is:

[0023]

[0024] in: For the first The approximate matrix of the inverse of the Hessian matrix during step iteration; For the first The approximate matrix of the inverse of the Hessian matrix during step iteration; For the first Step and the first The difference vector between decision vectors in each iteration; For the first Step and the first The difference vector of the gradient of the objective function between iterations; It is the identity matrix; superscript This represents the transpose operation of a matrix or vector.

[0025] Furthermore, during the online optimization process, the surge boundary margin of each compression unit is calculated in real time. When the surge boundary margin of any compression unit is lower than the preset warning threshold, a safety penalty term is applied to the objective function to shift the optimal solution away from the surge boundary.

[0026] Furthermore, during the online identification and updating of the heat transfer efficiency factor, a heat exchanger core thermal inertia compensation mechanism is introduced to transiently correct the steady-state parameters. This heat exchanger core thermal inertia compensation mechanism uses a transient energy balance equation including the time derivative to extract physical delay features, thereby obtaining the dynamic heat transfer efficiency factor. The calculation formula is:

[0027]

[0028] in: The quasi-steady-state heat transfer efficiency factor is calculated based on the current actual number of heat transfer units; The inherent thermal time constant of the heat exchanger core, in units of . The value is determined by the specific heat capacity, mass, and heat exchange area of ​​the heat exchanger core material. For the shell-and-tube intercooler, the value range is... to ; The rate of change of the quasi-steady-state heat transfer efficiency factor over time is determined by combining numerical differentiation with quasi-steady-state dynamics, based on real-time measurements of instantaneous mass flow rate and changes in state parameters at various temperature levels. The functional relationship between the above parameters is calculated in real time; in the thermodynamic coupling model, the dynamic heat transfer efficiency factor is used. The results of the quasi-steady-state model were used to correct the temperature transfer relationship between stages.

[0029] Furthermore, the imposed security penalties Calculate using the following formula:

[0030]

[0031] in: This represents the total number of compression stages. For the first Safety weighting factor for compression units; The preset warning threshold is set to a value of [value]. to Positive real numbers between; For the first Surge boundary margin of the compression unit, expressed as a percentage.

[0032] Furthermore, before each iteration of optimization, the historical optimal pressure ratio allocation record with the highest matching degree with the current working condition is retrieved from the pre-built historical working condition database, and this record is used as the initial value for the iteration.

[0033] Furthermore, when retrieving from the historical operating condition database, the similarity is assessed by calculating the weighted Euclidean distance between the current operating condition feature vector and the historical records. Differentiated weight factors are assigned to each feature dimension of the operating condition. The weight factors for the cooling water inlet temperature dimension and the exhaust mass flow rate demand dimension are both higher than the weight factor for the ambient atmospheric pressure dimension.

[0034] Furthermore, an extended Kalman filter is used to recursively process the deviation between the measured real-time state parameters and the output prediction values ​​of the thermodynamic coupling model, and a low-frequency trend component reflecting the drift of the equipment's physical characteristics is separated. When the low-frequency trend component meets the preset diagnostic conditions, the reference values ​​of the interstage flow resistance loss coefficient and the heat transfer efficiency factor are automatically corrected.

[0035] Furthermore, when constructing the thermodynamic coupling model, the physical properties of the compression medium are corrected in real time. The correction includes calculating the equivalent gas constant and equivalent adiabatic index of the wet air based on the temperature and humidity measurements at the intake port of the first-stage compression unit, and correcting the actual mass flow rate of the subsequent compression unit based on the condensate discharge of the interstage cooler.

[0036] In addition, the present invention also discloses a multi-stage air compressor airflow parameter iterative optimization system for performing the multi-stage air compressor airflow parameter iterative optimization method described above, including:

[0037] The data acquisition module is used to synchronously collect the intake pressure, intake temperature, exhaust pressure, exhaust temperature, instantaneous mass flow rate of each compression unit of the multi-stage air compressor at a preset sampling frequency, as well as the cooling water inlet temperature, outlet temperature and cooling water flow rate of each stage of the intercooler, to form real-time status parameters.

[0038] The parameter decoupling modeling module is used to construct a thermodynamic coupling model based on real-time state parameters. The interstage flow resistance loss coefficient and heat transfer efficiency factor within the model are both identified and updated online based on the real-time state parameters. The interstage pressure transfer relationship is corrected by the online identified and updated interstage flow resistance loss coefficient, and the interstage temperature transfer relationship is corrected by the online identified and updated heat transfer efficiency factor, thus obtaining a constraint space that reflects the current actual physical state of the equipment. The iterative optimization calculation module is used to perform online optimization within the constraint space using a superlinear convergent iterative method based on the second-order gradient information of the objective function, with the goal of minimizing the specific power of the whole machine. It solves the optimal pressure ratio allocation of each stage under the current operating conditions in real time and converts the optimal pressure ratio allocation into the exhaust pressure setpoint and speed setpoint of each stage.

[0039] The execution control module is used to receive the exhaust pressure setpoints and speed setpoints at each stage and drive the corresponding actuators to operate.

[0040] Furthermore, the iterative optimization calculation module has a built-in initial value retrieval unit, which is used to retrieve the historical optimal pressure ratio allocation record with the highest matching degree with the current working condition from the pre-built historical working condition database, and use the record as the initial value for iteration.

[0041] Furthermore, it also includes a fault diagnosis and model correction unit. This unit uses an extended Kalman filter to recursively process the deviation between the measured real-time state parameters of the data acquisition module and the output predicted values ​​of the parameter decoupling modeling module, and separates the low-frequency trend component that reflects the drift of the physical characteristics of the equipment. When the low-frequency trend component meets the preset diagnostic conditions, it automatically corrects the reference values ​​of the interstage flow resistance loss coefficient and the heat transfer efficiency factor.

[0042] Furthermore, the iterative optimization module applies a safety penalty term during the online optimization process, and the safety penalty term includes a safety weight factor. Based on the The phase trajectory rate of the compression unit's operating point moving towards the surge boundary is dynamically adaptively adjusted; the dynamic adaptive adjustment control law is executed according to the following formula:

[0043]

[0044] in: For the first The basic safety weight constant of the compression unit; The preset rate sensitivity coefficient; For the first The time derivative of the surge boundary margin of the compression unit; when the operating point approaches the surge boundary with an accelerating trend, the safety penalty term exhibits exponential nonlinear amplification.

[0045] Compared with the prior art, the present invention has the following beneficial effects:

[0046] This invention solves the technical problem of the disconnect between traditional static models and the actual equipment state by constructing a thermodynamic coupling model that can update the interstage flow resistance loss coefficient and heat transfer efficiency factor in real time. This model isomorphically maps the actual physical degradation state of the equipment to the mathematical optimization space. Based on the superlinear convergent iterative method of the second-order gradient information of the objective function, the optimization trajectory is guided by the local curvature geometric features of the target surface. This overcomes the oscillation and divergence of the first-order gradient method on the surface of the strongly nonlinear flow field equation. It can accurately solve the optimal pressure ratio allocation corresponding to the current physical conditions within a single control cycle. The whole machine operates near the theoretical optimal energy efficiency point under all operating conditions, effectively reducing the average specific power and significantly reducing the range of exhaust pressure fluctuations and shortening the system response delay.

[0047] Furthermore, this invention, by online identification and updating of interstage flow resistance loss coefficients, enables the constraint space to dynamically reflect the nonlinear increase in pipeline flow resistance caused by flow rate changes. The optimization results automatically offset the flow resistance effect with pressure ratio offset, improving adaptability across a wide operating range. By online identification and updating of the heat transfer efficiency factor, performance degradation such as cooling water scaling or water temperature fluctuations is detected in real time and converted into changes in interstage temperature constraints, eliminating optimization bias from its physical source. After introducing a heat exchanger core thermal inertia compensation mechanism, the dynamic heat transfer efficiency factor is obtained by correcting the transient energy balance equation containing time derivatives. This eliminates the phase deviation between the constraint space and the actual thermal boundary caused by the heat storage effect of the heat exchanger metal core under transient conditions, significantly improving the transient accuracy of the model under load steps.

[0048] The safety penalty term applied in the iterative optimization process of this invention has a safety weight factor that is dynamically and adaptively adjusted based on the phase trajectory rate. When the operating point accelerates and approaches the surge boundary, the penalty term is amplified exponentially, forming a dynamic repulsive force field that is sensitive to the approach rate. This achieves preventive suppression of surge stall risk within a unified optimization framework, eliminating the delay and inconsistency in the external switching between energy efficiency optimization and safety protection.

[0049] The initial value retrieval unit built into this invention extracts optimization records of similar operating conditions from a historical operating condition database using weighted Euclidean distance as initial values ​​for iteration. Combined with a differentiated dimension weighting mechanism, this significantly improves the iteration convergence speed under transient operating conditions and effectively suppresses optimization delays caused by sudden changes in operating conditions. Furthermore, the fault diagnosis and model correction unit uses an extended Kalman filter to separate low-frequency trend components characterizing the drift of physical properties and automatically corrects the model reference value in a closed-loop manner. This enables the system to continuously adapt to long-term degradation scenarios such as impeller fouling and cooler fouling, ensuring model matching accuracy and optimization performance throughout its entire lifecycle. Attached Figure Description

[0050] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.

[0051] Figure 1 This is a flowchart of the iterative optimization method for airflow parameters of a multi-stage air compressor according to the present invention.

[0052] Figure 2 This is a flowchart of the internal calculation process of a single control cycle of the iterative optimization calculation module of the present invention.

[0053] Figure 3 This is a flowchart of the fault diagnosis and model correction unit of the present invention.

[0054] Figure 4 This is a diagram of the system operation interface when using this invention. Detailed Implementation

[0055] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the embodiments of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0056] The following is in conjunction with the appendix Figures 1-4 The embodiments of the present invention will be described in detail below.

[0057] Example 1: Deployment structure of the multi-stage air compressor airflow parameter iterative optimization system of the present invention on a three-stage centrifugal air compressor unit. The unit is arranged sequentially along the gas flow direction as a first-stage compression unit, a first-stage intercooler, a second-stage compression unit, a second-stage intercooler, and a third-stage compression unit.

[0058] The sensor arrays of the data acquisition module are respectively located at the intake port of the first-stage compression unit, the exhaust port of the first-stage compression unit, the cooling water outlet of the first-stage intercooler, the intake port of the second-stage compression unit, the exhaust port of the second-stage compression unit, the cooling water outlet of the second-stage intercooler, the intake port of the third-stage compression unit, and the exhaust port of the third-stage compression unit. The sensor signals from all measuring points are collected into the parameter decoupling modeling module via a synchronous sampling card.

[0059] The system is no less than The system synchronously collects inlet pressure, inlet temperature, outlet pressure, outlet temperature, and instantaneous mass flow rate at preset sampling frequencies, as well as the inlet and outlet temperatures and flow rates of cooling water in the interstage coolers, forming real-time status parameters. After processing by a hardware anti-aliasing filter, the collected signals undergo analog-to-digital conversion via a synchronous sampling card, and the digital signals are transmitted to the central processing unit.

[0060] The execution logic flow is as follows:

[0061] Within a single control cycle, the central processing unit identifies and updates the interstage flow resistance loss coefficient and heat transfer efficiency factor online based on real-time state parameters, constructing a thermodynamic coupling model and constraint space reflecting the current actual physical state of the equipment. With the goal of minimizing the overall specific power, a superlinear convergent iterative method based on the second-order gradient information of the objective function is used to solve for the optimal pressure ratio allocation of each stage online within the current constraint space, simultaneously outputting the exhaust pressure setpoints and speed setpoints for each stage. These setpoints are then converted into speed commands for the variable frequency drive and closed-loop control target values ​​for the exhaust pressure of each stage, which are adjusted through the execution control module.

[0062] The iterative optimization calculation module receives the current operating condition constraint vector output by the parameter decoupling modeling module. The constraint vector includes the upper and lower limits of the allowable pressure ratio of each stage, the upper limit of the suction temperature under the current heat exchange efficiency condition, the upper limit of the current actual speed of the motor, and the interstage flow resistance pressure drop dynamically calculated by modifying the Fanning friction formula.

[0063] The iterative optimization module retrieves the record with the highest matching degree to the current working condition from the historical working condition database as the initial value for iteration, and then enters a superlinear convergent iterative loop. In each iteration, the gradient of the objective function and the Hessian matrix or its approximation matrix at the current decision point are calculated. The Armijo line search criterion is used to determine whether the step size meets the sufficient descent condition; if not, the step size is decayed until the condition is met. The iteration terminates when the residual vector magnitude falls below a preset threshold, and the optimal pressure ratio and corresponding speed setpoint for each stage are output. (Preset convergence threshold) Values .

[0064] During the iteration process, the iterative optimization calculation module continuously monitors the surge boundary margin. If the margin falls below the preset warning threshold... At that time, a safety penalty term is automatically included in the objective function, and the search direction is shifted towards the safe zone through geometric deformation of the penalty function. A preset warning threshold is also included. Values .

[0065] This embodiment implements the method of the present invention on a three-stage centrifugal air compressor unit, with the unit's rated exhaust pressure... Rated volumetric flow rate The rated power of the matching motor .

[0066] In the data acquisition module, pressure measurements at each level use response times of less than [time missing]. Full-scale accuracy not less than The high-frequency pressure sensing device uses Class A precision platinum resistance thermometers paired with high-precision transmitter circuits for temperature measurement at each stage, ensuring high temperature measurement accuracy. The interstage cooler cooling water flow rate adopts... Measurement with a high-precision electromagnetic flowmeter, sampling frequency set to [value missing]. All sensor signals undergo analog-to-digital conversion via a synchronous sampling card with a unified clock synchronization trigger mechanism, adjusting the conversion resolution. The synchronous sampling card can lock the physical quantities of pressure, temperature, and flow at the same moment, eliminating phase errors caused by signal transmission delays.

[0067] After obtaining the real-time state parameters, the parameter decoupling modeling module performs the following processing. Define the first... Stage compression unit pressure ratio for:

[0068]

[0069] in: For the first The intake pressure of the primary compression unit, in units of ; For the first The exhaust pressure of the compression unit is expressed in units of... ; Pick These correspond to the first, second, and third level compression units, respectively.

[0070] No. Multistage compression unit variable efficiency Based on the current measured inlet and outlet temperatures and pressure ratios, the following is determined in real time through the polytropic compression process relationship:

[0071]

[0072] in: For the first intake temperature of the primary compression unit, in units of ; For the first The exhaust temperature of the compression unit is expressed in units of _____. ; The gas adiabatic index is generated in real-time by an embedded property compensation subroutine based on dew point data measured by the integrated temperature and humidity transmitter at the intake of the first-stage compression unit, avoiding enthalpy calculation errors caused by treating air as an ideal dry gas. The equivalent gas constant for moist air is also mentioned. The intake air moisture content is calculated based on dew point data and determined in real time using the ideal gas mixing law, eliminating the bias introduced in density and internal energy calculations by treating air as a single-component ideal gas.

[0073] According to the law of conservation of energy, the first The compression unit consumes shaft power. Calculate using the following formula:

[0074]

[0075] in: Instantaneous mass flow rate, unit: The flow rate is directly measured by the intake flow meter of the first-stage compression unit; This is the specific heat capacity under constant pressure, in units of... The values ​​are obtained by interpolating the current stage average temperature and pressure from the physical property database.

[0076] As the gas flows through each stage of the intercooler, a phase change occurs, resulting in precipitation. The actual mass flow rate of the primary compression unit needs to be compensated for in real time based on the condensate discharge rate.

[0077]

[0078] in: The first signal returned by the condensate flow meter downstream of the steam trap Interstage cooler condensate discharge rate, in units of The step-by-step flow correction mechanism can eliminate the systematic overestimation of the power prediction of the downstream impeller by the traditional constant flow assumption, so that the pressure ratio distribution under humid conditions matches the actual physical load.

[0079] In handling inter-level coupling relationships, the first Level and First Between the compression units, there exists an interstage channel consisting of an intercooler and connecting piping. intake pressure of the primary compression unit Determined by the following formula:

[0080]

[0081] in: For the first Level to No. The interstage flow resistance loss coefficient is dimensionless. In this embodiment, the interstage flow resistance loss coefficient... Dynamic calculations were performed by modifying the Fanning friction formula:

[0082]

[0083] in: For the first The exhaust port of the first stage compression unit to the first The equivalent piping length of the intake port of the primary compression unit, in units of ; Equivalent pipe diameter, unit: ; The average density of the gas inside the pipeline, in units of ; The average gas velocity in the pipeline, in units of ; The Darcy-Weisbach friction factor is updated in real time using the Colebrook formula based on the current Reynolds number and the equivalent roughness of the pipe wall.

[0084] In this embodiment, the interstage flow resistance loss coefficient It becomes a dynamic variable that changes with flow rate and gas state. An increase in mass flow rate leads to an increase in the interstage flow resistance loss coefficient. When the nonlinear growth occurs, the iterative optimization algorithm will reflect this change in the constraint space. The optimization result will automatically reduce the pressure ratio of the upper stage and increase the pressure ratio of the lower stage, so as to offset the impact of the increase in flow resistance on the overall efficiency by dynamically shifting the pressure ratio.

[0085] No. intake temperature of the primary compression unit Determined by the following formula:

[0086]

[0087] in: For the first Interstage cooler inlet water temperature, in units of ; For the first Interstage cooler heat transfer efficiency factor, dimensionless, range of values to .

[0088] In this embodiment, the heat transfer efficiency factor pass The NTU method utilizes real-time measured cooling water and gas side temperatures and flow rates to perform online identification. Based on the real-time temperature and flow signals from both the cooling water and compressed air sides, it calculates the actual number of heat transfer units (NTUs) in the heat exchanger and, using the counter-current heat transfer relationship, inversely solves for the heat transfer efficiency factor at the current moment. .

[0089] Compared to empirical models with fixed heat exchange efficiency, this method can detect the heat exchange performance degradation caused by cooling water scaling and water temperature fluctuations in real time, and convert it into changes in interstage temperature constraints. This ensures that the optimization input constraints always match the actual thermal state of the equipment, eliminating optimization bias caused by physical degradation and isomorphic breakage of the mathematical model from the physical root.

[0090] Within the constraint space constructed by the thermodynamic coupling model, the iterative optimization module performs optimization with the objective of minimizing the specific power of the entire system. The objective function for the specific power of the entire system is as follows: Defined as:

[0091]

[0092] in: This refers to the additional power consumption of the intermediate cooling system, including the power consumption of the cooling water pump and the cooling fan, in units of... The power is obtained from real-time power measurements. The mass flow rate at the exhaust port of the third-stage compression unit is expressed in units of... ; The gas density at the exhaust port of the third-stage compression unit is given in units of... Denominator term The volumetric flow rate of the air compressor's real-time exhaust is used to measure the energy consumption per unit of air production. This definition ensures the real-time performance of power ratio calculations and facilitates online evaluation by optimization algorithms.

[0093] The superlinear convergent iterative method used in this embodiment, based on the second-order gradient information of the objective function, is the Newton-Raphson iterative method with Hessian matrix correction. A three-dimensional decision vector is defined at the current iteration point. objective function The gradient vector of the decision vector is denoted as... The Hessian matrix is ​​denoted as In each iteration, the search direction is calculated using the following formula. :

[0094]

[0095] When the Hessian matrix is ​​not positive definite at the current point, the system performs structured regularization correction by injecting small orthogonal perturbations along the diagonal, ensuring that the search direction always points towards the descent direction of the objective function. Update step size. The maximum step size that satisfies the sufficient descent condition is determined by the Armijo line search criterion, as follows:

[0096]

[0097] in: As a preset parameter, the value in this embodiment is [value]. The iteration terminates when the magnitude of the iterative residual vector satisfies the following convergence criterion:

[0098]

[0099] in: For the first Inequality constraint functions; For the corresponding Lagrange multipliers; To preset the convergence threshold, this embodiment sets the value to [value]. ; To constrain the number of constraints.

[0100] Before each search in the iterative process, the iterative optimization module synchronously performs a surge safety check. Define the... Surge boundary margin of a compression unit for:

[0101]

[0102] in: For the current number Mass flow rate of the compression unit, in units of ; The pressure ratio corresponding to the current speed surge boundary mass flow rate, in units of The surge boundary margin of any first-stage compression unit is obtained through interpolation from the compressor's general characteristic curve dataset stored within the control system. Below the preset warning threshold When iterating to optimize the objective function Additional security penalties will be imposed. The calculation formula is as follows:

[0103]

[0104] in: For the first Safety weighting factor for compression units; To preset the warning threshold, this embodiment uses a value of [value]. .

[0105] The optimal pressure ratio vector obtained after iterative convergence This will be converted into exhaust pressure setpoints and speed setpoints for each stage. The intake end of the first-stage compression unit is directly connected to the atmosphere, and the intake pressure changes with the ambient atmospheric pressure. Its exhaust pressure setpoint is determined by... The pressure is determined in conjunction with the measured atmospheric pressure. The intake pressure of the second and third stage compression units is affected by the output of the preceding stage and the interstage flow resistance. An independent closed-loop pressure control loop is used, with the iteratively calculated exhaust pressure setpoint as the adjustment target. The speed setpoint is determined by mapping the pressure ratio of the third stage compression unit to the compressor characteristic curve under the current intake conditions, and also serves as the reference speed for the first two stage variable frequency drives.

[0106] The execution control module receives the above set values ​​via an industrial fieldbus. The main drive motor uses space vector pulse width modulation technology to convert the speed set value into a frequency converter drive signal, achieving precise motor speed tracking. Each stage of the intake guide vanes is driven by a stepper motor to adjust the guide vane opening.

[0107] The iterative optimization module has a built-in initial value retrieval unit to improve the system response speed under transient conditions. During continuous system operation, the optimization results of each convergence and the current operating condition feature vector will be synchronously stored in the multi-dimensional operating condition database. The operating condition feature vector covers six dimensions: ambient atmospheric pressure, ambient atmospheric temperature, atmospheric relative humidity, user pipeline pressure setpoint, cooling water inlet temperature, and exhaust mass flow rate requirement.

[0108] When a new round of optimization begins, the initial value retrieval unit calculates the weighted Euclidean distance between the current operating condition feature vector and the historical data, and extracts the value with the smallest distance. Historical pressure ratio optimization results Values The initial value for this iteration is obtained by weighting the values ​​according to the reciprocal of the distance. In the weighted Euclidean distance calculation, the weighting factors for each dimension differ. The weighting factors for the dimensions of cooling water inlet temperature and exhaust mass flow rate demand are higher than those for the dimension of ambient atmospheric pressure. This differentiated weighting is consistent with the laws of physical characteristics.

[0109] Most similar in database When the weighted Euclidean distance between historical records and the current operating condition exceeds a preset similarity threshold, the initial value retrieval unit will abandon historical data retrieval and adopt a cold-start initial value derived analytically based on the physical model. This initial value retrieval mechanism can significantly improve the iteration convergence speed, requiring only a few steps in most continuous operation scenarios. Convergence can be achieved in one iteration, effectively suppressing the optimization delay caused by sudden changes in operating conditions.

[0110] In practical implementation, the initial cold start value is determined according to the principle of equal pressure ratio allocation, that is, the pressure ratio of each stage is: in, For the first The initial pressure ratio of the compression unit is dimensionless. The target exhaust pressure for the entire machine, in units of ; This is the intake pressure of the first-stage compression unit, in units of... ; To compress the total number of levels.

[0111] This embodiment is in On a three-stage centrifugal compressor unit Continuous operation comparison test.

[0112] Comparative Example 1: A traditional control scheme combining fixed pressure ratio allocation with PID exhaust pressure regulation, where the pressure ratio of each stage is fixed at the first stage. Level 2 Level 3 The tests covered typical operating conditions such as diurnal temperature variation, cooling water temperature rise, and downstream load fluctuations. The test results are shown in Table 1.

[0113] Table 1. Comparison of operational data between Example 1 and Comparative Example 1;

[0114]

[0115] Test data shows that the solution in this embodiment outperforms Comparative Example 1 in all six performance indicators. The average power-to-weight ratio of the entire machine is reduced. This improvement stems from the precise matching of the thermodynamic coupling model, the efficient optimization of the superlinear convergent iterative method, and the proactive compensation of the dynamic pressure ratio offset strategy. The optimization of indicators such as exhaust pressure fluctuation range, system response delay, and peak pressure drop due to sudden load changes benefits from the feedforward compensation capability of the iterative optimizer and the rapid convergence characteristics of the initial value retrieval mechanism.

[0116] Example 2: Based on Example 1, this example further clarifies the working logic of the fault diagnosis and model correction unit.

[0117] Specifically as follows:

[0118] In each control cycle, the parameter decoupling modeling module calculates the predicted temperature and pressure values ​​from the thermodynamic coupling model and compares them point-by-point with the measured parameters from the data acquisition module to generate a deviation vector. An extended Kalman filter recursively processes this deviation vector to separate the low-frequency trend components that characterize the drift of the equipment's physical properties.

[0119] When the cumulative amplitude and duration of the low-frequency trend component meet the preset diagnostic conditions, the fault diagnosis and model correction unit automatically starts the model parameter identification program. With the goal of minimizing the mean square error between the model prediction value and the measured value, it corrects the reference values ​​of the interstage flow resistance loss coefficient and the heat transfer efficiency factor.

[0120] This closed-loop correction mechanism can adapt to long-term equipment degradation scenarios such as impeller fouling and cooler fouling, continuously ensuring the matching degree between the thermodynamic coupling model and the actual physical state of the equipment. The remaining technical solutions in this embodiment are the same as those in Embodiment 1.

[0121] Example 3: This example is basically the same as Example 1, except that this example provides an alternative to the superlinear convergent iterative method based on the second-order gradient information of the objective function, which is used to adapt to application scenarios where the floating-point operation resources of the industrial control motherboard are limited.

[0122] Example 1 uses the complete Hessian matrix to analytically derive the second-order gradient information, which has a high computational load. This example uses the BFGS quasi-Newton method to approximate the inverse of the Hessian matrix, eliminating the need to explicitly calculate the second-order partial derivatives of the objective function and reducing the computational load.

[0123] Define the evolution of the decision vector. Gradient divergence of objective function The approximate matrix of the inverse of the Hessian matrix Updated via BFGS formula:

[0124]

[0125] The search direction is calculated from the inverse of the current approximate Hessian matrix, and the step size control still adopts the Armijo line search criterion.

[0126] This scheme can reduce the computational load on the control unit and improve the transient feedback suppression capability of small disturbances in the pipeline network while maintaining second-order convergence characteristics. The remaining technical solutions in this embodiment are the same as those in Embodiment 1.

[0127] Example 4: Based on the thermodynamic coupling model and iterative optimization framework of Example 1, this example introduces a heat exchanger core thermal inertia compensation mechanism and a surge phase trajectory rate sensing adaptive safety weight adjustment mechanism to solve the model mismatch problem under transient load step conditions.

[0128] In practical implementation, the heat exchanger core has a limited heat capacity. When the load fluctuates drastically, the core's heat storage effect causes the exhaust temperature response to lag behind changes in mass flow rate, resulting in a steady-state... The heat transfer efficiency factor identified by the NTU method will deviate from the actual transient heat transfer capacity. This is the core reason why the constraint space deviates from the real thermal boundary under transient conditions.

[0129] The heat exchanger core thermal inertia compensation mechanism aligns with the steady-state heat transfer efficiency factor through a transient energy balance equation that includes a time derivative. After correction, the dynamic heat transfer efficiency factor is obtained. The calculation formula is:

[0130]

[0131] in: The inherent thermal time constant of the heat exchanger core, in units of . The specific heat capacity, mass, and heat exchange area of ​​the heat exchanger core material are determined. For the large-capacity shell-and-tube intercooler configured in this embodiment, Values The dynamic heat transfer efficiency factor will replace the quasi-steady-state results in the calculation of interstage temperature transfer relationships, eliminating the model phase lag caused by core thermal inertia, and ensuring that the thermodynamic coupling model always matches the real thermodynamic boundary during millisecond-level load steps.

[0132] This embodiment upgrades the adjustment method of the surge safety weight factor from static threshold detection to phase space trajectory rate sensing. The time derivative of the surge boundary margin is calculated using numerical differentiation. Safety weight factor Based on the exponential adaptive adjustment of the rate of change, the calculation formula is as follows:

[0133]

[0134] in: For the first The basic safety weight constant of the compression unit; The preset rate sensitivity coefficient is set to a value of [value missing] in this embodiment. When the operating point accelerates towards the surge boundary, the safety penalty term amplifies exponentially, forming a dynamic repulsive force field to mitigate surge risks in advance.

[0135] This embodiment conducts a full-load to half-load step test on a three-stage centrifugal air compressor unit equipped with a large-capacity shell-and-tube intercooler. The load step time is controlled within... The test results are shown in Table 2.

[0136] Table 2 Comparison of the performance of Example 4 in dealing with transient load step changes;

[0137]

[0138] Test data shows that the thermal inertia compensation mechanism can significantly reduce the prediction error of transient temperature constraint boundary, and the adaptive safety weight adjustment mechanism can significantly improve the safety margin of surge boundary. The combination of the two technologies can shorten the convergence time of pressure ratio allocation and improve the smoothness of the optimization trajectory.

[0139] The thermal inertia compensation mechanism and adaptive safety weight adjustment mechanism described in this embodiment can be implemented in any combination with the fault diagnosis function in Embodiment 2 and the BFGS quasi-Newton method in Embodiment 3. The remaining technical solutions are the same as in Embodiment 1.

[0140] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0141] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. It should be noted that any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An iterative optimization method for airflow parameters of a multi-stage air compressor, characterized in that, include: The system synchronously collects the intake pressure, intake temperature, exhaust pressure, exhaust temperature, and instantaneous mass flow rate of each compression unit of the multi-stage air compressor at a preset sampling frequency, as well as the inlet and outlet temperatures and flow rates of the cooling water in each stage of the intercooler, to form real-time status parameters. A thermodynamic coupling model is constructed based on the real-time state parameters. The interstage flow resistance loss coefficient and heat transfer efficiency factor in the model are both identified and updated online based on the real-time state parameters. The interstage pressure transmission relationship is corrected by the online identified and updated interstage flow resistance loss coefficient, and the interstage temperature transmission relationship is corrected by the online identified and updated heat transfer efficiency factor. A constraint space that can reflect the current actual physical state of the equipment is constructed. With minimizing the specific power of the whole machine as the objective function, an online optimization method based on the second-order gradient information of the objective function is used in the constraint space to determine the optimal pressure ratio allocation of each stage under the current working condition in real time. The optimal pressure ratio distribution obtained from the solution is converted into exhaust pressure setpoints and speed setpoints for each stage, and then output to the actuator.

2. The method for iterative optimization of airflow parameters in a multi-stage air compressor according to claim 1, characterized in that, The interstage flow resistance loss coefficient is determined dynamically by combining the modified Fanning friction formula with the real-time calculated gas Reynolds number and pipeline roughness. No. Level to No. Interstage flow resistance loss coefficient The following formula is used for calculation: in: For the first The exhaust port of the first stage compression unit to the first The equivalent piping length of the intake port of the primary compression unit, in units of ; The equivalent diameter of the pipeline is given in units of 1. ; The average density of the gas inside the pipeline, in units of ; The average gas velocity in the pipeline, in units of ; For the first The exhaust pressure of the compression unit is expressed in units of... ; The Darcy-Weisbach friction factor is updated in real time using the Colebrook formula based on the current Reynolds number and the equivalent roughness of the pipe wall.

3. The method for iterative optimization of airflow parameters in a multi-stage air compressor according to claim 1, characterized in that, The heat exchange efficiency factor is obtained through The NTU method utilizes real-time measured cooling water temperature and flow rate, along with gas temperature and flow rate, to perform online identification. The identification process includes calculating the actual number of heat transfer units in the current heat exchanger, and then, based on the counter-current heat transfer relationship, reversibly solving for the heat transfer efficiency factor at the current moment. The nth... The heat transfer efficiency factor of the intercooler is .

4. The method for iterative optimization of airflow parameters in a multi-stage air compressor according to claim 1, characterized in that, The superlinear convergent iterative method based on the second-order gradient information of the objective function is the Newton-Raphson iterative method. The iterative method uses the Armijo line search criterion to achieve adaptive step size control. Update step size Select the maximum step size that satisfies the following conditions: in: The objective function is... This is the current decision vector; Indicating the search direction; This is the transpose of the objective function with respect to the gradient of the decision vector; These are preset parameters, and their value range is [value range missing]. to .

5. The method for iterative optimization of airflow parameters in a multi-stage air compressor according to claim 1, characterized in that, The superlinear convergent iterative method based on the second-order gradient information of the objective function is a quasi-Newton method. This quasi-Newton method approximates the inverse of the Hessian matrix using the BFGS formula and employs the Armijo line search criterion to perform adaptive step size control. The BFGS formula is: in: For the first The approximate matrix of the inverse of the Hessian matrix during step iteration; For the first The approximate matrix of the inverse of the Hessian matrix during step iteration; For the first Step and the first The difference vector between decision vectors in each iteration; For the first Step and the first The difference vector of the gradient of the objective function between iterations; It is the identity matrix; superscript This represents the transpose operation of a matrix or vector.

6. The method for iterative optimization of airflow parameters in a multi-stage air compressor according to claim 1, characterized in that, During the online optimization process, the surge boundary margin of each compression unit is calculated in real time. When the surge boundary margin of any compression unit is lower than the preset warning threshold, a safety penalty term is applied to the objective function to shift the optimal solution away from the surge boundary.

7. The method for iterative optimization of airflow parameters in a multi-stage air compressor according to claim 1, characterized in that, In the process of online identification and updating of heat transfer efficiency factors, a heat exchanger core thermal inertia compensation mechanism is introduced to transiently correct steady-state parameters. This mechanism uses a transient energy balance equation including time derivatives to extract physical delay characteristics, thereby obtaining the dynamic heat transfer efficiency factor. The calculation formula is: in: The quasi-steady-state heat transfer efficiency factor is calculated based on the current actual number of heat transfer units; The inherent thermal time constant of the heat exchanger core, in units of . The value is determined by the specific heat capacity, mass, and heat exchange area of ​​the heat exchanger core material. For the shell-and-tube intercooler, the value range is... to ; The rate of change of the quasi-steady-state heat transfer efficiency factor over time is determined by combining numerical differentiation with quasi-steady-state dynamics, based on real-time measurements of instantaneous mass flow rate and changes in state parameters at various temperature levels. The functional relationship between the above parameters is calculated in real time; in the thermodynamic coupling model, the dynamic heat transfer efficiency factor is used. The results of the quasi-steady-state model were used to correct the temperature transfer relationship between stages.

8. The method for iterative optimization of airflow parameters in a multi-stage air compressor according to claim 6, characterized in that, The imposed safety penalties Calculate using the following formula: in: This represents the total number of compression stages. For the first Safety weighting factor for compression units; The preset warning threshold is set to a value of [value]. to Positive real numbers between; For the first Surge boundary margin of the compression unit, expressed as a percentage.

9. The method for iterative optimization of airflow parameters in a multi-stage air compressor according to claim 1, characterized in that, Before each iteration of optimization, the historical optimal pressure ratio allocation record with the highest matching degree with the current working condition is retrieved from the pre-built historical working condition database, and this record is used as the initial value for the iteration.

10. A multi-stage air compressor airflow parameter iterative optimization system, used to execute the multi-stage air compressor airflow parameter iterative optimization method according to any one of claims 1-9, characterized in that, include: The data acquisition module is used to synchronously collect the intake pressure, intake temperature, exhaust pressure, exhaust temperature, instantaneous mass flow rate of each compression unit of the multi-stage air compressor at a preset sampling frequency, as well as the cooling water inlet temperature, outlet temperature and cooling water flow rate of each stage of the intercooler, to form real-time status parameters. The parameter decoupling modeling module is used to construct a thermodynamic coupling model based on real-time state parameters. The interstage flow resistance loss coefficient and heat transfer efficiency factor in the model are both identified and updated online based on real-time state parameters. The interstage pressure transfer relationship is corrected by the online identified and updated interstage flow resistance loss coefficient, and the interstage temperature transfer relationship is corrected by the online identified and updated heat transfer efficiency factor, so as to obtain a constraint space that reflects the current actual physical state of the equipment. The iterative optimization calculation module is used to perform online optimization within the constraint space using a superlinear convergent iterative method based on the second-order gradient information of the objective function, with the goal of minimizing the specific power of the whole machine. It solves the optimal pressure ratio allocation of each stage under the current operating condition in real time and converts the optimal pressure ratio allocation into the exhaust pressure setpoint and speed setpoint of each stage. The execution control module is used to receive the exhaust pressure setpoints and speed setpoints at each stage and drive the corresponding actuators to operate.

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