An Adaptive Online Optimization Method for Dynamic Hydraulic Balance of Pipeline Networks

Abstract

This invention relates to the field of adaptive online optimization technology for dynamic hydraulic balance in pipeline networks, and discloses an adaptive online optimization method for dynamic hydraulic balance in pipeline networks. By constructing a node-pipeline topology model and defining control variables and thresholds, data input standardization is achieved; valve opening and flow rate are collected in real time to construct hydraulic impedance and spectral matrices, accurately reflecting dynamic operating conditions; the spectral matrix is ​​decomposed to extract global and local oscillation mode features, assigning differentiated weights to adjustments; residuals are calculated based on water demand and flow rate, and tolerance thresholds and projection verification are set, triggering subsequent adjustments only when there is a true imbalance; the direction of opening adjustment is clarified based on spectral analysis and sensitivity assessment to avoid blind action; the optimal step size is analytically solved and limited, balancing convergence speed and impact suppression; valve opening is updated by branch and issued in a closed loop, achieving continuous online optimization and automated control, significantly improving the real-time performance, stability, and intelligence level of the pipeline network.

Description

Technical Field

[0001] This invention relates to the field of adaptive online optimization technology for dynamic hydraulic balance of pipe networks, specifically an adaptive online optimization method for dynamic hydraulic balance of pipe networks. Background Technology

[0002] With the acceleration of urbanization, the scale of urban water distribution networks is constantly expanding, with the number of nodes and pipeline length increasing exponentially. The network operation exhibits strong time-varying, nonlinear, and distributed characteristics. Traditional optimization of network hydraulic balance often relies on static design models or empirical rules, including pump station scheduling based on empirical curves, network energy-saving optimization based on linear programming, and offline optimization based on heuristic algorithms (such as genetic algorithms and ant colony algorithms). These methods typically treat the network as a static flow system, assuming relatively smooth fluctuations in demand and pressure, and neglecting the dynamic characteristics of rapid changes in node demand, water hammer effects, and lags in valve opening adjustments within the water supply system.

[0003] The commonly used EPANET software in existing technologies provides hydraulic simulation and pollutant tracking functions, but its solver is mainly designed for network equations under steady-state or quasi-steady-state conditions, making it difficult to meet the needs of online optimization at the millisecond to second level. If simulation and optimization are tightly coupled for real-time control, the computational load is enormous, and the accuracy of the pipeline network model and boundary conditions are limited, easily leading to convergence difficulties or solution distortion due to initial condition deviations. Some studies have attempted to apply model predictive control (MPC) to water distribution networks, but high-dimensional variables and complex constraints make it difficult to complete online solutions within a short period, and it lacks adaptability to system disturbances and measurement noise. In addition, existing dynamic equilibrium methods mostly rely on empirical fitting of flow-pressure relationships, or only consider a single objective (such as energy minimization or pressure equilibrium), ignoring the multimodal oscillation characteristics of the pipeline network and the coupling effect of valve openings; when demand changes abruptly or water quality changes, they cannot respond quickly, easily leading to risks such as node overpressure or pipeline siltation. Meanwhile, traditional adjustment methods lack a unified online monitoring and hierarchical alarm mechanism, making it impossible to conduct effective residual tolerance checks before valve adjustment. If the adjustment direction is wrong, it may oscillate repeatedly and fail to converge to the desired equilibrium.

[0004] Therefore, this study aims to propose an adaptive online optimization method for dynamic hydraulic balance in pipeline networks. It digitally models the network nodes and pipeline structures, constructs hydraulic impedance matrices and node coupling matrices using real-time collected opening and flow data, and performs spectral decomposition to reveal the system's oscillation modes and energy distribution characteristics. Combining node-level residual calculation and projection verification strategies, it accurately determines the degree of supply-demand imbalance and modal importance, then allocates the direction and amplitude of flow adjustment according to the weights of different modes. Through linear step-size analytical solution and amplitude limiting constraints, it achieves precise and stable valve opening updates, ultimately constructing a closed-loop online control mechanism. Summary of the Invention

[0005] This invention provides an adaptive online optimization method for dynamic hydraulic balance of pipe networks, which helps to solve the problems mentioned in the background art.

[0006] This invention provides the following technical solution: an adaptive online optimization method for dynamic hydraulic balance of pipe networks, comprising:

[0007] S1. Establish a pipeline network topology that includes nodes and pipelines, define pipeline network variables and related thresholds, and form a basic data model that can be used for dynamic analysis.

[0008] S2. Real-time acquisition of operating parameters of each pipeline in the pipeline network, and construction of hydraulic impedance matrix and node spectrum matrix based on the acquired data;

[0009] S3. Perform spectral decomposition on the node spectral matrix to extract eigenvalues ​​and corresponding eigenvectors;

[0010] S4. Based on the water demand and pipeline flow data of each node at the current moment, calculate the hydraulic flow residual of each node;

[0011] S5. Set a tolerance threshold for the calculated residuals, perform tolerance judgment and projection verification. If the residuals exceed the tolerance range, perform projection analysis and verify the system response under each mode. If it fails, issue an alarm and perform feature decomposition analysis again.

[0012] S6. Based on the spectral analysis results and the driving flow adjustment process, determine the opening adjustment direction, analyze the sensitivity of pipeline flow to valve opening, and calculate the adjustment amount and adjustment direction.

[0013] S7. By analyzing and calculating the step size and setting the limit, the optimal solution and range constraint of the adjustment step size are performed. If the step size parameter is abnormal, an alarm message is issued and the calculation is returned to recalculate; if the step size is within the preset range, the opening adjustment is performed.

[0014] S8. Based on the adjustment results, update the valve opening according to the branch conditions and send the latest control quantity to the corresponding valve.

[0015] Optionally, the establishment of a pipeline network topology including nodes and pipelines, the definition of pipeline network variables and related thresholds, and the formation of a basic data model that can be used for dynamic analysis specifically include:

[0016] Set the discrete control cycle index to ;in, It is a set of non-negative integers;

[0017] Obtain the total number of pipeline nodes, denoted as Set the network node set as Obtain the total number of pipelines including valves, denoted as . ; Set up a pipeline including valves as ;in, It is a set of positive integers;

[0018] Construct the directed incidence matrix:

[0019] ;

[0020] in, This is used to describe the connection relationship between nodes and pipelines; For node index, the value range is: ; Index of pipelines including valves;

[0021] Acquire pipeline The nominal hydraulic resistance constant is denoted as ;

[0022] Set the minimum allowable valve opening as follows: ;

[0023] Initialize valve opening vector ;in, For a moment pipeline Valve opening ratio, .

[0024] Optionally, the real-time acquisition of operating parameters of each pipeline in the pipeline network, and the construction of a hydraulic impedance matrix and a node spectrum matrix based on the acquired data, specifically includes:

[0025] Read valve opening , forming vectors ;

[0026] Calculate pipeline At any moment Instantaneous hydraulic resistance ;

[0027] Constructing a resistance diagonal matrix ;in, Place the elements in parentheses in order on the diagonal, and set the rest to zero; for OK A matrix of real numbers in columns;

[0028] Construct the node spectrum matrix: ;in, for OK A matrix of real numbers in columns; It is a Laplace matrix for inter-node coupling.

[0029] Optionally, the step of performing spectral decomposition on the node spectral matrix to extract eigenvalues ​​and corresponding eigenvectors specifically includes:

[0030] Find spectral decomposition: , ;in, For the first Modal eigenvalues; For the corresponding unit eigenvector;

[0031] Sort the feature values ​​in ascending order: .

[0032] Optionally, the step of calculating the hydraulic flow residual of each node based on the water demand and pipeline flow data of each node at the current moment specifically includes:

[0033] Time node Water demand is denoted as ,time pipeline Traffic is recorded as ;

[0034] compute nodes At any moment flow residual ;

[0035] Combining all residuals into a vector .

[0036] Optionally, the step of setting a tolerance threshold for the calculated residuals, performing tolerance judgment and projection verification, and if the residuals exceed the tolerance range, then performing projection analysis and verifying the system response under each mode, and if it fails, issuing an alarm and re-performing feature decomposition analysis, specifically including:

[0037] Let the residual tolerance threshold be... ,and ;

[0038] like If the result is positive, proceed to step S8; otherwise, calculate the residual in step S8. Projection coefficients under modal conditions ;

[0039] Let the projection reconstruction tolerance be ,and ;

[0040] like If the alarm is triggered, return to step S4; otherwise, proceed to step S6.

[0041] Optionally, the step of determining the valve opening adjustment direction based on the spectral analysis results and the driving flow adjustment process, analyzing the sensitivity of pipeline flow to valve opening, and calculating the adjustment amount and direction specifically includes:

[0042] Calculate the normalization constant ;

[0043] like If the alarm spectrum matrix is ​​all zeros, there is no valid mode, and the process terminates; otherwise, the calculation proceeds sequentially:

[0044] Calculate pipeline Raw flow adjustment :

[0045] ;

[0046] Let the minimum sensitivity threshold be ,and ;

[0047] Calculate pipeline Flow rate sensitivity to opening degree ;

[0048] Calculate the initial adjustment amount of the opening. ;

[0049] Calculate the maximum absolute opening adjustment amount ;

[0050] Calculate the normalized opening adjustment direction :

[0051] ;like The alarm indicates no valid direction and returns to step S4.

[0052] Optionally, the step size is calculated analytically and a limit is set to optimize and constrain the adjustment step size. If the step size parameter is abnormal, an alarm message is issued and the calculation is returned for recalculation; if the step size is within the preset range, the opening adjustment is performed, specifically including:

[0053] Calculate residuals by direction projection increment ;

[0054] Set the objective function as ;in, Step size factor;

[0055] Find the analytical optimal step size ;

[0056] Let the maximum step size be ,and ;

[0057] like If the alarm is triggered, the process returns to step S4.

[0058] like Then take ;in, This is the step size factor for adjusting the opening.

[0059] Optionally, the step of updating the valve opening according to the branch conditions based on the adjustment results and issuing the latest control quantity to the corresponding valve specifically includes:

[0060] like Then let ;

[0061] Otherwise, let ;

[0062] Will Issued to the valve for execution;

[0063] make Return to step S2 and continue online optimization.

[0064] The present invention has the following beneficial effects:

[0065] 1. By accurately depicting the relationships between nodes and pipelines in the water supply and drainage network using a directed correlation matrix, and simultaneously defining various variables and thresholds required for network operation, this innovative approach achieves unified modeling of topology information and control parameters. Unlike traditional methods that rely on manual drawing or simple table maintenance, this matrix-based method stores network scale, node quantity, and information on pipelines including valves in a structured manner, avoiding parameter omissions and format inconsistencies, and providing clear and unified basic data for subsequent matrix operations and spectral decomposition. On the one hand, the standardized data model reduces deployment and maintenance costs and improves applicability to large-scale networks; on the other hand, accurate network mapping ensures the correctness and stability of subsequent calculations, fundamentally solving adjustment errors caused by topology inconsistencies, and providing a solid data foundation for the entire online optimization process.

[0066] 2. In traditional pipeline network analysis, hydraulic calculations often rely on static models or periodic offline analysis, lacking real-time response to dynamic changes in valve opening. This innovative solution combines real-time acquired valve opening data with pipeline resistance constants, constructing a hydraulic impedance diagonal matrix and a node coupling spectrum matrix through online calculation. This accurately reflects the dynamic characteristics of each pipeline resistance changing with opening and comprehensively describes the flow-pressure coupling relationship between nodes. Real-time matrix construction enables online hydraulic model updates, accurately reflecting on-site conditions without offline calibration; simultaneously, the spectrum matrix provides complete input for subsequent spectral decomposition, ensuring the accuracy of feature extraction. Compared to existing static or semi-dynamic models, this approach improves the timeliness and precision of pipeline network hydraulic analysis, resolving issues of system response lag and model error accumulation.

[0067] 3. Traditional pipeline network optimization often only adjusts the entire network as a whole, making it difficult to identify flow and pressure fluctuation patterns in different regions or frequency bands. This innovative solution performs spectral decomposition on the node coupling spectrum matrix, extracting the characteristic intensities and corresponding vectors of multiple oscillation modes to achieve a dual characterization of both low-frequency, large-scale fluctuations and high-frequency, local disturbances in the system. On the one hand, residuals can be projected and allocated according to different modes, allowing subsequent adjustments to give greater weight to important modes; on the other hand, it can distinguish between global and local effects, avoiding local congestion or inability to make targeted adjustments due to neglecting high-frequency disturbances, thus improving the accuracy and stability of the adjustment strategy. Compared with existing methods that rely solely on empirical rules or single indicators, this step achieves in-depth analysis of the pipeline network's dynamic behavior, truly enabling site-specific and mode-specific control.

[0068] 4. The proposed solution calculates the flow surplus of each node based on real-time node water demand and pipeline flow data, and forms a residual vector from all surpluses to quantitatively characterize the supply-demand balance deviation of all nodes in the entire network. Unlike traditional methods that only count overall water volume differences or judge based on a single node, this method achieves node-level granularity, clearly identifying the specific location and degree of hydraulic imbalance. This provides accurate input data for subsequent tolerance assessment and modal projection; it also helps operators quickly locate problem areas, facilitating the development of more targeted adjustment strategies; compared to existing methods that rely on pipeline network simulation or experience-based judgment, it improves early warning efficiency and fault location speed, solving the previous problem of difficulty in timely detection and quantification of node imbalance.

[0069] 5. To avoid frequent adjustments due to measurement noise or slight fluctuations, this solution innovatively sets a tolerance threshold for node residuals and verifies them through modal projection reconstruction when the threshold is exceeded to determine whether to initiate the adjustment process. This not only filters out false alarms caused by minor daily fluctuations, reducing unnecessary computational burden and equipment wear, but also ensures that adjustments are triggered only when there is a genuine imbalance and the numerical quality is reliable, thus improving the robustness of the algorithm. Compared with existing methods that generally use fixed thresholds or no verification mechanism, this step balances sensitivity and stability, solving the problems of excessively frequent or missed adjustments.

[0070] 6. The proposed solution combines the residual projection results of modal components with their corresponding modal weights to calculate the original flow adjustment for each pipeline, and determines the adjustment direction based on the sensitivity assessment of flow to valve opening. This approach breaks through the traditional crude adjustment method of simply increasing or decreasing flow, achieving targeted flow correction. Sensitivity analysis eliminates ineffective or excessive adjustments, ensuring the scientific nature of opening adjustments; simultaneously, different adjustment weights are assigned to different modes, balancing global and local optimization objectives. Compared to existing techniques that rely on manual experience to fit sensitivity or simple proportional adjustments, this step improves adjustment effectiveness and system stability, solving the problem of difficulty in simultaneously meeting the needs of different areas in complex pipeline networks.

[0071] 7. To ensure both rapid and stable adjustments, this scheme introduces an analytical solution method for the first time. The objective function relating the residual projection increment and the step size factor is optimized in a closed loop to obtain the optimal step size value, and a maximum opening change limit is set. Analytical solutions reduce the computational load of iterative searches, enabling efficient online computation; the limit constraint prevents pressure fluctuations or pipeline shocks caused by single opening changes. Compared to existing methods that often use empirical step sizes or simple linear increments, this approach balances convergence speed and safety, resolving the problems of overshoot oscillations or slow convergence that easily occur in online pipeline optimization.

[0072] 8. Based on the aforementioned adjustment results and branch conditions, the opening degree of each valve is updated in real time, and control commands are sent to the actuators to form a complete online closed-loop control mechanism. Through continuous iteration and real-time feedback, the pipeline network can automatically adapt to load changes and continuously maintain hydraulic balance. Simultaneously, the branch logic and threshold judgment are organically combined, allowing for strategy switching under special conditions, further enhancing the system's flexibility and safety. Compared to traditional periodic manual scheduling or single offline optimization, this step achieves truly 24 / 7, network-wide automated online control, solving the pain points of delays and poor response times in manual scheduling. Attached Figure Description

[0073] Figure 1 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0074] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0075] Example, refer to Figure 1 An adaptive online optimization method for dynamic hydraulic balance of pipe networks, comprising:

[0076] S1. Establish a pipeline network topology that includes nodes and pipelines, define pipeline network variables and related thresholds, and form a basic data model that can be used for dynamic analysis.

[0077] S2. Real-time acquisition of operating parameters of each pipeline in the pipeline network, and construction of hydraulic impedance matrix and node spectrum matrix based on the acquired data;

[0078] S3. Perform spectral decomposition on the node spectral matrix to extract eigenvalues ​​and corresponding eigenvectors;

[0079] S4. Based on the water demand and pipeline flow data of each node at the current moment, calculate the hydraulic flow residual of each node;

[0080] S5. Set a tolerance threshold for the calculated residuals, perform tolerance judgment and projection verification. If the residuals exceed the tolerance range, perform projection analysis and verify the system response under each mode. If it fails, issue an alarm and perform feature decomposition analysis again.

[0081] S6. Based on the spectral analysis results and the driving flow adjustment process, determine the opening adjustment direction, analyze the sensitivity of pipeline flow to valve opening, and calculate the adjustment amount and adjustment direction.

[0082] S7. By analyzing and calculating the step size and setting the limit, the optimal solution and range constraint of the adjustment step size are performed. If the step size parameter is abnormal, an alarm message is issued and the calculation is returned to recalculate; if the step size is within the preset range, the opening adjustment is performed.

[0083] S8. Based on the adjustment results, update the valve opening according to the branch conditions and send the latest control quantity to the corresponding valve.

[0084] By establishing a pipeline network topology including nodes and pipelines and defining control variables and thresholds, the problem of inconsistent algorithm inputs caused by the difficulty in unifying the basic data model in traditional online pipeline optimization is solved. By collecting operating parameters such as valve opening and pipeline flow in real time and constructing hydraulic impedance matrices and node coupling spectrum matrices, the shortcomings of static models in reflecting changes in on-site operating conditions are overcome, achieving an accurate description of the dynamic characteristics of the pipeline network. By performing spectral decomposition on the spectrum matrix and extracting modal eigenvalues ​​and eigenvectors, the problem of previous optimization methods being unable to distinguish between large-scale global fluctuations and small-scale local disturbances is solved, enabling adjustment measures to assign differentiated weights to different oscillation modes. Furthermore, by basing adjustments on water demand and... The steps of calculating residuals from flow data and setting tolerance thresholds and performing projection verification filter measurement noise and minor fluctuations, avoiding over-adjustment or underreporting risks, and ensuring that subsequent processes are triggered only when there is a genuine imbalance. The steps of using spectral decomposition results to drive flow adjustment and opening direction determination provide scientific direction guidance and sensitivity analysis, avoiding system oscillations caused by blindly increasing or decreasing flow. The steps of analytically solving for the step size and setting amplitude constraints efficiently obtain the optimal opening increment, accelerating convergence and preventing the impact of large adjustments on the pipeline network. Finally, the steps of updating valve openings under branch conditions and issuing control commands in a closed loop achieve continuous online optimization and automated closed-loop control. Through the seamless integration of these steps, the problems of slow response, poor adjustment accuracy, and oscillations in traditional pipeline network optimization are solved, improving the system's real-time performance, stability, and intelligence, and contributing to energy conservation, loss reduction, and safe and reliable operation of urban pipeline networks.

[0085] The establishment of a pipeline network topology including nodes and pipelines, the definition of pipeline network variables and related thresholds, and the formation of a basic data model that can be used for dynamic analysis specifically include:

[0086] Set the discrete control cycle index to ;in, It is a set of non-negative integers; it defines the time scale for discrete control, which is used for subsequent data acquisition and iteration.

[0087] Obtain the total number of pipeline nodes, denoted as Set the network node set as Obtain the total number of pipelines including valves, denoted as . ; Set up a pipeline including valves as ;in, Given a set of positive integers; determine the system size, and all subsequent matrix dimensions are based on this. and ;

[0088] Construct the directed incidence matrix:

[0089] ;

[0090] in, This is used to describe the connection relationship between nodes and pipelines; For node index, the value range is: ; The pipeline index includes valves; the connection direction between each pipeline and the two nodes is accurately described in matrix form, which facilitates subsequent matrix operations;

[0091] Acquire pipeline The nominal hydraulic resistance constant is denoted as Quantify the physical properties of pipelines to calculate hydraulic impedance;

[0092] Set the minimum allowable valve opening as follows: ;

[0093] Initialize valve opening vector ;in, For a moment pipeline Valve opening ratio, Ensure that the valve still has a minimum flow rate when it is closed, and initialize the system.

[0094] By setting discrete control cycle indices and time scales to unify the steps of data acquisition and iteration sequence, the problems of control confusion and data mismatch caused by unclear control cycle division were solved. By obtaining and defining the total number of network nodes and the total number of pipelines including valves, and constructing corresponding node and pipeline sets, the system scale and matrix dimension were accurately determined, avoiding computational crashes caused by model scale estimation errors. By describing the connectivity between nodes and pipelines in the form of a directed correlation matrix, the traditional scattered and difficult-to-automate processing of topology information was overcome, providing standardized and verifiable topology data for subsequent matrix operations. The steps of defining the nominal hydraulic resistance constant of the pipeline and quantifying its physical characteristics resolve calculation errors caused by missing resistance parameters or assumption mistakes, achieving objective and accurate resistance estimation. By setting the minimum allowable valve opening and initializing the valve opening vector, the potential risks of no flow or control failure due to complete valve closure are avoided, while ensuring the system has basic flow capacity during initial startup. These steps organically combine discretized time-series management, topology modeling, physical parameter quantification, and valve initialization, forming a systematic and repeatable basic data model. This provides robust and reliable data support for the entire online optimization process, improving the algorithm's robustness and applicability.

[0095] The real-time acquisition of operating parameters of each pipeline in the pipeline network, and the construction of a hydraulic impedance matrix and a node spectrum matrix based on the acquired data, specifically includes:

[0096] Read valve opening , forming vectors Obtain the current pipeline opening for subsequent impedance calculations;

[0097] Calculate pipeline At any moment Instantaneous hydraulic resistance Describe the real-time impact of valve regulation on pipeline impedance;

[0098] Constructing a resistance diagonal matrix ;in, Place the elements in parentheses in order on the diagonal, and set the rest to zero; for OK A real matrix of columns; integrate the impedances of each pipeline into a diagonal matrix for easier unified calculation;

[0099] Construct the node spectrum matrix: ;in, for OK A matrix of real numbers in columns; This is the Laplace-type matrix for inter-node coupling; forming the Laplace-type coupling matrix between nodes prepares for subsequent spectral decomposition.

[0100] By reading valve openings and forming a unified vector, centralized management of the real-time opening status of each pipeline is achieved, solving the problem of subsequent computational chaos caused by scattered data storage. By calculating the instantaneous hydraulic resistance of the pipelines, the impact of valve regulation on resistance changes is clearly quantified, overcoming the shortcomings of traditional models where resistance estimation often relies on experience or simplification assumptions. By constructing a resistance diagonal matrix to efficiently integrate the impedance data of each pipeline, a structured and directly computable input is provided for subsequent matrix operations, avoiding the performance waste of multiple loop readings and matching. By constructing a node spectrum matrix to describe the coupling relationship between nodes, hydraulic impedance and node coupling information are innovatively fused, forming an efficient matrix for spectral decomposition, overcoming the limitation that constructing a coupling matrix or impedance matrix alone cannot obtain overall dynamic information. Through these steps, real-time extraction and efficient integration of pipeline network operating parameters are achieved, providing an accurate and complete input matrix for subsequent spectral decomposition and feature extraction, improving the response speed and analytical accuracy of the dynamic hydraulic model to changes in operating conditions.

[0101] The spectral decomposition of the node spectral matrix to extract eigenvalues ​​and corresponding eigenvectors specifically includes:

[0102] Find spectral decomposition: , ;in, For the first Modal eigenvalues, also called modal intensities or oscillation frequency indices, physically quantify the characteristics of the first modal. The strength / rigidity of the network oscillation mode or the hydro-pressure coupling mode, small The mode corresponds to low-frequency, wide-range flow-pressure fluctuations; large... This corresponds to high-frequency, small-range local fluctuations; in the scheme, it is used to assign different adjustment weights to the residual projection. This allows for smaller step sizes in high-frequency modes, ensuring system stability. The corresponding unit eigenvectors are used to extract the system's inherent oscillation modes and their intensities.

[0103] Sort the feature values ​​in ascending order: Organizational modal priority is determined by frequency or energy from low to high.

[0104] By performing spectral decomposition on the node spectral matrix and extracting modal eigenvalues ​​and corresponding eigenvectors, this method directly correlates network oscillation modes and intensities with the system's intrinsic dynamic behavior for the first time. This overcomes the shortcomings of traditional optimization, which focuses only on a single indicator and struggles to distinguish between different oscillation modes. The method of differentiating between low-frequency, large-scale fluctuations and high-frequency, local disturbances effectively ensures that the adjustment strategy can address both network-wide and local imbalances separately, avoiding local congestion or network-wide oscillations caused by single-frequency band control. Furthermore, by sorting modal eigenvalues ​​by energy or frequency from low to high and prioritizing them, the method enables flexible application of oscillation modes in the weight allocation of adjustments, improving regulation efficiency and stability. These steps, which delve into the physical information contained in the spectral matrix, provide a scientific basis for subsequent residual projection and adjustment decisions, enhancing the accuracy and reliability of pipeline network optimization and representing a significant breakthrough in intelligent pipeline network control.

[0105] The calculation of the hydraulic flow residual at each node based on the current water demand and pipeline flow data includes:

[0106] Time node Water demand is denoted as ,time pipeline Traffic is recorded as ;

[0107] compute nodes At any moment flow residual ;

[0108] Combining all residuals into a vector Quantify the current supply and demand imbalance at each node to provide a basis for adjustments.

[0109] By calculating the node flow residuals based on real-time data of water demand and pipeline flow at each node, a precise quantification of the supply-demand deviation across the entire network is achieved. This solves the problem that traditional methods can only roughly estimate the overall difference and cannot pinpoint the imbalance nodes. By unifying the calculated residuals into a residual vector, a structured data input is provided for subsequent tolerance determination and modal projection, avoiding the efficiency loss from multiple scattered calculations and data recombination. By closely integrating field measurement data with model calculations through the above steps, not only can supply-demand imbalances at each node be detected in a timely manner, but also a precise basis can be provided for subsequent adjustment strategies. This improves the speed of problem location and data processing efficiency, and is conducive to achieving efficient online closed-loop optimization.

[0110] The process involves setting a tolerance threshold for the calculated residuals, performing tolerance judgment and projection verification. If the residuals exceed the tolerance range, projection analysis is performed and the system response under each mode is verified. If the verification fails, an alarm is issued and feature decomposition analysis is performed again. Specifically, this includes:

[0111] Let the residual tolerance threshold be... ,and Function: If If the supply and demand balance at the node is considered to be within an acceptable range, the opening adjustment for this cycle will be skipped. Impact of the value: Too small, and adjustments will be frequently triggered, causing system oscillations and high computational load; Too large, and significant imbalances may be overlooked, affecting water supply quality. Basis for value selection: Based on the network size and daily flow fluctuation range. Recommended value: Use the maximum daily flow of a typical node. For example, the maximum demand of a certain node Optional .

[0112] like If the residual is small enough, skip to step S8 to save resources; otherwise, calculate the residual at step S8. Projection coefficients under modal conditions Decompose the residuals into each model and quantify the contribution of each model.

[0113] Let the projection reconstruction tolerance be ,and Function: To test spectral projection Compared with the true residual The degree of agreement between the values, if the error exceeds Then resampling or an alarm will occur. Impact of value: Too small, strict verification may lead to frequent recalculation due to numerical noise; too large, it may ignore mode reconstruction errors, resulting in incorrect direction adjustments. Basis for value selection: Based on the accuracy of numerical calculation and the magnitude of the residual. Recommendation for value selection: Use a typical value of the residual. like average ,but .

[0114] like If the error is detected, an alarm is triggered and the process returns to step S4; otherwise, proceed to step S6; ensure numerical accuracy and prevent any abnormal data from causing incorrect adjustments.

[0115] By setting reasonable tolerance thresholds for the residual vector and performing tolerance judgment, false alarms caused by measurement errors and short-term fluctuations are effectively filtered out, solving the problems of system oscillation and wasted computing resources caused by frequent invalid adjustments. By performing modal projection reconstruction and verifying projection errors when the residual exceeds the limit, subsequent optimization is only triggered when the modal information is reliable and there is a real imbalance, avoiding erroneous adjustments caused by outliers or noisy data. Through the dual gatekeeping mechanism of tolerance judgment and projection verification, strict control over the adjustment triggering conditions is achieved, enhancing the robustness and stability of the algorithm, reducing the risk of misadjustment and missed adjustment, and providing reliable quality assurance for online pipeline optimization.

[0116] Based on the spectral analysis results and the driving flow adjustment process, the valve opening adjustment direction is determined, the sensitivity of pipeline flow to valve opening is analyzed, and the adjustment amount and direction are calculated. Specifically, this includes:

[0117] Calculate the normalization constant Standardize the damping of each mode to make its dimensions dimensionless;

[0118] like If the alarm spectrum matrix is ​​all zeros, there is no valid mode, and the process terminates to avoid division by zero and invalid adjustments; otherwise, the calculation proceeds sequentially:

[0119] Calculate pipeline Raw flow adjustment :

[0120] Calculate the flow correction amount based on the weights of each mode and the residual projection;

[0121] Let the minimum sensitivity threshold be ,and Function: To ensure safety when the flow rate is extremely low or the opening is close to zero. The value should not be zero, avoiding division by zero or directional stagnation. Impact of the value: Too small, and the original formula remains in place, risking division by zero; too large, artificially amplifying minute flow changes may lead to misadjustment. Basis for value selection: Based on the minimum measurable flow rate accuracy on site. Recommended value: Slightly higher than the minimum resolution of the flow sensor, such as... ,but .

[0122] Calculate pipeline Flow rate sensitivity to opening degree It describes the linear approximate gain of flow rate on opening degree to prevent zero flow failure.

[0123] Calculate the initial adjustment amount of the opening. Convert flow rate adjustment into opening adjustment to ensure consistent dimensions;

[0124] Calculate the maximum absolute opening adjustment amount ;

[0125] Calculate the normalized opening adjustment direction :

[0126] ;like An alarm is triggered indicating no valid direction, and the process returns to step S4; direction information is extracted and amplitude is limited to... Ensure consistent step size application.

[0127] By using spectral decomposition results to drive flow adjustment direction and combining it with pipeline flow sensitivity analysis of valve opening, targeted and scientific adjustment guidance is achieved, solving the problems of blind adjustment and easy oscillation in traditional experience-based or single-proportion regulation. By calculating the original flow adjustment amount and converting it into the opening adjustment amount, the flow target and valve control are effectively linked, avoiding execution errors caused by numerical mismatch. Through the above steps, the adjustment needs of each pipeline are accurately grasped and appropriate adjustment is given, which not only ensures the promotion effect of hydraulic balance of the whole network, but also prevents pressure shock caused by excessive local adjustment, thus improving the stability and reliability of system operation.

[0128] The process involves calculating the step size analytically and setting limits to optimize and constrain the adjustment step size. If the step size parameter is abnormal, an alarm is issued and the calculation is restarted. If the step size is within the preset range, the opening is adjusted. Specifically, this includes:

[0129] Calculate residuals by direction projection increment ;Evaluate the linear effect of unit opening adjustment on residuals;

[0130] Set the objective function as ;in, Let be the step size factor; define a curve of the sum of squared residuals as a function of the step size to facilitate analytical minimization;

[0131] Find the analytical optimal step size ;beg Find the minimum point to obtain the optimal adjustment range;

[0132] Let the maximum step size be ,and Function: Limits the maximum percentage of valve opening updates per cycle, preventing large adjustments from causing system overshoot or oscillation. Impact of Value: Too small a value, while allowing for rapid response, can easily cause pressure fluctuations; too large a value results in slow convergence and a lagging system response. Basis for Value: Based on the valve's maximum safe opening variation range; for example, the valve manufacturer recommends that a single adjustment should not exceed [a certain value]. Then take Recommended value: First set it to... Then, make slight adjustments based on the actual response speed and pressure stability.

[0133] like If the alarm is triggered, the process returns to step S4.

[0134] like Then take ;in, The step size factor for opening adjustment controls the overall opening update range in this cycle, preventing it from being too large (leading to oscillation) or too small (ineffective adjustment); avoiding system instability or ineffectiveness caused by excessively large or small step sizes.

[0135] By constructing an objective function from the residual projection increment and step size factor and solving for the analytically optimal step size, closed-loop optimization of the adjustment range is achieved, solving the problems of high computational cost and slow convergence in traditional iterative search methods. By setting a maximum opening change limit, pressure fluctuations and hydraulic shocks in the pipeline network caused by a large one-time adjustment are avoided. Through the above steps, both adjustment efficiency and safety are ensured, enabling online optimization to quickly eliminate imbalances and maintain stable system pressure, providing an efficient and safe guarantee for automated pipeline network control.

[0136] The step of updating the valve opening according to the branch conditions based on the adjustment results and issuing the latest control quantity to the corresponding valves specifically includes:

[0137] like Then let ;

[0138] Otherwise, let ;

[0139] By combining step size and direction, the valve opening can be adjusted or maintained in a bounded manner;

[0140] Will Issued to the valve for execution;

[0141] make Return to step S2 and continue online optimization;

[0142] Once one closed loop is completed, the next cycle begins.

[0143] By updating the opening adjustment results differently based on branch conditions and issuing real-time updates to the valve actuators, closed-loop control of the adjustment process is achieved, solving the problem of not being able to continuously iterate and correct online. The step of iteratively returning for subsequent optimization ensures that the pipeline network can continuously adapt to changes in water usage, avoiding the drawback of losing monitoring and control after a one-time adjustment. Through a complete online closed-loop scheduling mechanism, the system can operate 24 / 7 and automatically, minimizing manual intervention while ensuring water supply quality, thus improving the intelligence level and operational efficiency of the pipeline network.

[0144] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0145] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. An adaptive online optimization method for dynamic hydraulic balance of pipe networks, characterized in that, include: S1. Establish a pipeline network topology that includes nodes and pipelines, define pipeline network variables and related thresholds, and form a basic data model that can be used for dynamic analysis. Set the discrete control cycle index to ;in, It is a set of non-negative integers; S2. Real-time acquisition of operating parameters of each pipeline in the pipeline network, and construction of hydraulic impedance matrix and node spectrum matrix based on the acquired data; S3. Perform spectral decomposition on the node spectral matrix to extract eigenvalues ​​and corresponding eigenvectors; No. Modal eigenvalues The corresponding unit eigenvector is ; S4. Based on the water demand and pipeline flow data of each node at the current moment, calculate the hydraulic flow residual of each node; node At any moment The flow residual is Combine all residuals into a vector ; For node index, the value range is: ; This represents the total number of pipeline nodes. S5. Set a tolerance threshold for the calculated residuals, perform tolerance judgment and projection verification. If the residuals exceed the tolerance range, perform projection analysis and verify the system response under each mode. If it fails, issue an alarm and perform feature decomposition analysis again. The process involves setting a tolerance threshold for the calculated residuals, performing tolerance judgment and projection verification. If the residuals exceed the tolerance range, projection analysis is performed and the system response under each mode is verified. If the verification fails, an alarm is issued and feature decomposition analysis is performed again. Specifically, this includes: Let the residual tolerance threshold be... ,and ; like If the result is positive, proceed to step S8; otherwise, calculate the residual in step S8. Projection coefficients under modal conditions ; Let the projection reconstruction tolerance be ,and ; like If the alarm is triggered, return to step S4; otherwise, proceed to step S6. S6. Based on the spectral analysis results and the driving flow adjustment process, determine the opening adjustment direction, analyze the sensitivity of pipeline flow to valve opening, and calculate the adjustment amount and adjustment direction. S7. By analyzing and calculating the step size and setting the limit, the optimal solution and range constraint of the adjustment step size are performed. If the step size parameter is abnormal, an alarm message is issued and the calculation is returned to recalculate; if the step size is within the preset range, the opening adjustment is performed. S8. Based on the adjustment results, update the valve opening according to the branch conditions and send the latest control quantity to the corresponding valve.

2. The adaptive online optimization method for dynamic hydraulic balance of a pipe network according to claim 1, characterized in that, The establishment of a pipeline network topology including nodes and pipelines, the definition of pipeline network variables and related thresholds, and the formation of a basic data model that can be used for dynamic analysis specifically include: Set the discrete control cycle index to ;in, It is a set of non-negative integers; Obtain the total number of pipeline nodes, denoted as Set the network node set as Obtain the total number of pipelines including valves, denoted as . ; Set up a pipeline including valves as ;in, It is a set of positive integers; Construct the directed incidence matrix: ； in, This is used to describe the connection relationship between nodes and pipelines; For node index, the value range is: ; Index of pipelines including valves; Acquire pipeline The nominal hydraulic resistance constant is denoted as ; Set the minimum allowable valve opening as follows: ; Initialize valve opening vector ;in, For a moment pipeline Valve opening ratio, .

3. The adaptive online optimization method for dynamic hydraulic balance of a pipe network according to claim 2, characterized in that, The real-time acquisition of operating parameters of each pipeline in the pipeline network, and the construction of a hydraulic impedance matrix and a node spectrum matrix based on the acquired data, specifically includes: Read valve opening , forming vectors ; Calculate pipeline At any moment Instantaneous hydraulic resistance ; Constructing a resistance diagonal matrix ;in, Place the elements in parentheses in order on the diagonal, and set the rest to zero; for OK A real matrix of columns; Construct the node spectrum matrix: ;in, for OK A real matrix of columns; It is a Laplace matrix for the coupling between nodes.

4. The adaptive online optimization method for dynamic hydraulic balance of a pipe network according to claim 3, characterized in that, The spectral decomposition of the node spectral matrix to extract eigenvalues ​​and corresponding eigenvectors specifically includes: Find spectral decomposition: , ;in, For the first Modal eigenvalues; For the corresponding unit eigenvector; Sort the feature values ​​in ascending order: .

5. The adaptive online optimization method for dynamic hydraulic balance of a pipe network according to claim 4, characterized in that, The calculation of the hydraulic flow residual at each node based on the current water demand and pipeline flow data includes: Time node Water demand is denoted as ,time pipeline Traffic is recorded as ; compute nodes At any moment flow residual ; Combining all residuals into a vector .

6. The adaptive online optimization method for dynamic hydraulic balance of a pipe network according to claim 5, characterized in that, Based on the spectral analysis results and the driving flow adjustment process, the valve opening adjustment direction is determined, the sensitivity of pipeline flow to valve opening is analyzed, and the adjustment amount and direction are calculated. Specifically, this includes: Calculate the normalization constant ; like If the alarm spectrum matrix is ​​all zeros, there is no valid mode, and the process terminates; otherwise, the calculation proceeds sequentially: Calculate pipeline Raw flow adjustment : ； Let the minimum sensitivity threshold be ,and ; Calculate pipeline Flow rate sensitivity to opening degree ; Calculate the initial adjustment amount of the opening. ; Calculate the maximum absolute opening adjustment amount ; Calculate the normalized opening adjustment direction : ;like The alarm indicates no valid direction and returns to step S4.

7. The adaptive online optimization method for dynamic hydraulic balance of a pipe network according to claim 6, characterized in that, The process involves calculating the step size analytically and setting limits to optimize and constrain the adjustment step size. If the step size parameter is abnormal, an alarm is issued and the calculation is restarted. If the step size is within the preset range, the opening is adjusted. Specifically, this includes: Calculate residuals by direction projection increment ; Set the objective function as ;in, Step size factor; Find the analytical optimal step size ; Let the maximum step size be ,and ; like If the alarm is triggered, the process returns to step S4. like Then take ;in, This is the step size factor for adjusting the opening.

8. The adaptive online optimization method for dynamic hydraulic balance of a pipe network according to claim 7, characterized in that, The step of updating the valve opening according to the branch conditions based on the adjustment results and issuing the latest control quantity to the corresponding valves specifically includes: like Then let ; Otherwise, let ; Will Issued to the valve for execution; make Return to step S2 and continue online optimization.

Images