An indoor air-borne environmental element source position optimization method based on an adjoint equation

Abstract

The application discloses an indoor airborne environmental element source position optimization method based on an adjoint equation, and belongs to the technical field of indoor environment control and heating ventilation air conditioning. The airborne environmental element includes an airborne matter element transported with air flow and a thermal environmental element transferred by air flow. The method constructs an indoor space physical model and solves an air flow field to obtain a velocity vector and an effective transmission diffusion coefficient; the distribution of the airborne environmental element is simulated based on a forward scalar transmission equation; a target function is constructed according to a target area regulation and control requirement and a virtual source term of an adjoint equation is generated; the adjoint scalar field is obtained by reversely solving the adjoint scalar transmission equation and is mapped into a sensitivity field; the target space position of the airborne environmental element source is determined in the filtered sensitivity field by removing the unarrangeable area through a feasible region mask, and the release intensity is reversely solved. The application can be used for pollution source backstepping, disinfectant release, air conditioner air supply outlet arrangement and local cold and heat source deployment.

Description

Technical Field

[0001] This invention relates to the fields of indoor environmental control, heating, ventilation and air conditioning (HVAC), computational fluid dynamics (CFD), and intelligent building technologies. Specifically, it relates to an optimization method for determining the spatial release location of indoor airborne environmental element sources (including matter and thermal energy) using adjoint equations. Background Technology

[0002] In modern built environments, the precise control of airborne environmental elements directly impacts human health, comfort, and system energy consumption. This field primarily involves two categories of physical problems: mass transfer (such as determining the optimal release point of disinfectants in pandemic prevention scenarios, or inferring pollution sources in environmental monitoring); and heat transfer (such as determining the optimal location of air conditioning vents or auxiliary heat sources during heating or cooling to achieve rapid temperature regulation and uniform distribution). Therefore, rapidly and accurately determining the spatial release location of airborne environmental element sources is a core requirement for achieving efficient indoor environmental control.

[0003] Currently, existing technologies typically employ trial-and-error methods or heuristic algorithms (such as Genetic Algorithm (GA) and Particle Swarm Optimization (PSO)) to determine the aforementioned source locations. For example, invention patent CN103049612A (publication date: April 17, 2013) discloses a method for optimizing building indoor environments based on model reduction technology. This method utilizes a genetic algorithm (GA) combined with CFD software to search for optimal air conditioning supply parameters and performs forward iterative calculations using a CFD solver to find the optimal solution. Another example is invention patent CN112577159B (authorization announcement date: February 22, 2022), which discloses an intelligent energy-saving control method and device for air conditioning based on human thermal comfort. It proposes using particle swarm optimization and genetic algorithms to iteratively optimize human thermal comfort and air conditioning energy consumption. Meanwhile, existing conventional solutions usually establish separate models for mass diffusion and heat transfer, solving them independently.

[0004] However, the aforementioned existing technologies have the following technical problems in practical engineering applications:

[0005] 1. Forward iterative optimization leads to long computation time, making it difficult to meet real-time requirements: Heuristic algorithms require hundreds or thousands of forward iterations by continuously calling CFD software. Due to the unsteady turbulent diffusion involved in indoor airflow, the computational load of a single simulation is large, resulting in an exponential increase in the total computation cycle, making it unsuitable for emergency response scenarios requiring rapid decision-making, such as sudden pollution disinfection.

[0006] 2. Heat and mass transfer processes are modeled independently, lacking a unified mathematical solution framework: From the perspective of fluid dynamics, scalar transport (mass) and energy transport (heat) in low-speed airflow follow formally isomorphic governing equations. Existing technologies model these processes as independent domains, failing to leverage their isomorphism to simplify calculations, resulting in repetitive system development and poor compatibility of solution algorithms.

[0007] 3. Spatial discretization search is prone to getting trapped in local optima and ignores the continuity of the flow field: Traditional algorithms usually only search and match within a pre-defined set of discrete points (such as ceiling grid nodes). This spatial discretization method easily misses minute airflow structures in continuous space (such as the core point of the jet entrainment zone), making it difficult for the algorithm output to reach the theoretically optimal global position.

[0008] 4. Pure theoretical simulation lacks engineering feasibility constraints: Existing optimization models do not fully incorporate the physical interference conditions of the actual indoor environment. The optimal spatial coordinates calculated by these models may coincide with the interior of indoor furniture, building walls, or pedestrian walkways, making it impossible to install physical equipment at the optimized release locations, thus hindering subsequent engineering deployment and construction. Summary of the Invention

[0009] A computer-executed method for optimizing the location of indoor airborne environmental elements based on adjoint equations includes the following steps:

[0010] Step S1: Construct a physical model of the indoor space, solve the flow field of indoor air flow, and obtain the full-field velocity vector data and effective transmission diffusion coefficient data;

[0011] Step S2: Based on the set initial conditions, solve the forward scalar transport equation in the time domain [0, T] to obtain the forward distribution field of indoor airborne environmental elements as a function of time; the airborne environmental elements include airborne substance concentration, air temperature or air enthalpy.

[0012] Step S3: Based on the specific optimization task requirements, construct an objective function J that reflects the control performance index of the indoor target area; based on the variational principle, use the Fréchet derivative of the objective function with respect to the scalar variables of the airborne environmental elements to construct a virtual source term for the accompanying scalar transport equation.

[0013] Step S4: In the time domain [0, T], using the velocity vector data and effective transmission diffusion coefficient data, and driven by the virtual source term, solve the accompanying scalar transmission equation in reverse time to obtain the full-field accompanying scalar field;

[0014] Step S5: Map the entire field of the accompanying scalar field to generate a sensitivity field. The sensitivity value at any spatial location is determined by the accompanying scalar value corresponding to that location. Filter the sensitivity field using a preset feasible region mask. Select the spatial coordinates in the filtered sensitivity field that allow the objective function to reach its extreme value as the target spatial location of the airborne environmental element source.

[0015] Furthermore, this invention covers six core optimization tasks:

[0016] 1. Maximize transport efficiency: The objective function is the integral of the cumulative quantity, which is used to find the efficient point that achieves the maximum coverage of the target area with the minimum source input. It is suitable for scenarios such as efficient disinfection and rapid heating.

[0017] 2. Optimize distribution uniformity: The objective function is the variance integral, which is used to find the equilibrium point that makes the concentration or temperature distribution more uniform in the target area. It is suitable for scenarios such as comfort air conditioning and fragrance release.

[0018] 3. Precisely match the target value: The objective function is the integral of the sum of squared deviations, used to find the control point that can maintain the target setpoint.

[0019] 4. Minimize energy release or release cost: Based on the premise that the target area meets the standards, minimize the total release intensity or energy consumption of the source, which is applicable to scenarios such as HVAC and industrial purification.

[0020] 5. Minimize extreme value deviation in the target area: Focus on suppressing the maximum out-of-range value or the minimum under-of-range value in the target area to avoid local failure. It is suitable for scenarios such as computer rooms and operating rooms that are sensitive to local environmental deviations.

[0021] 6. Achieve stable compliance status in the shortest time: Achieve stable compliance in the target area in a relatively short time, suitable for rapid response scenarios such as pollution leakage disinfection and emergency cooling of computer rooms.

[0022] In addition, the target spatial location of the airborne environmental element source can also be the location of a virtual release source that causes anomalies in the airborne environmental element, used to reverse the source of pollution or thermal anomalies; it can also be a test location that characterizes the average air age, thermal residence time or airflow dead zone, used to identify inefficient areas in indoor ventilation or thermal environment control.

[0023] Compared with the prior art, the present invention has the following advantages:

[0024] Leveraging the mathematical properties of the adjoint method, gradient information at any point in a continuous space can be obtained with only one forward computation and one backward computation. Compared to traditional genetic algorithms that require hundreds or thousands of CFD simulations, this method significantly reduces computation time, making real-time optimization possible.

[0025] This invention innovatively establishes a universal solution model for airborne environmental factors. This is achieved by adjusting the turbulent Schmidt number (Sc) in the effective transport coefficient. t (for matter) or the Prandtl number of turbulence (Pr) t (Regarding heat), a single system can solve multiple problems such as pollutant tracing, disinfectant placement, radiator layout, and air conditioning vent optimization, and has extremely high commercial scalability.

[0026] The system employs a "feasibility region masking" technique to constrain the mathematically optimal solution to a physically feasible range. The system outputs coordinates that avoid the influence of furniture and building structures, providing direct guidance for construction or equipment deployment.

[0027] Unlike traditional algorithms that search for discrete points, this method solves the sensitivity field in a continuous grid space, which can capture key control points in complex airflow structures (such as vortices and jets) and ensure that the true global optimum is found.

[0028] Meanwhile, this invention integrates multiple objective functions within the same accompanying sensitivity solution framework, including maximizing transport efficiency, optimizing distribution uniformity, accurately matching target values, minimizing energy release, controlling extreme value deviations, and optimizing stable achievement time. It can also be extended to anomaly source back-calculation, average air age analysis, thermal residence time analysis, and airflow dead zone testing. Therefore, this invention can cover various engineering scenarios such as pollution control, disinfection site deployment, air conditioning vent optimization, localized cold and heat source deployment, and indoor environmental diagnostics, demonstrating good versatility and engineering applicability. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the process for optimizing the location of indoor airborne environmental elements based on the adjoint equation.

[0030] Figure 2 This is a schematic diagram of the feasible region mask principle.

[0031] Figure 3 A graph showing the comparison of algorithm optimization effects.

[0032] Figure 4 This is a three-dimensional sensitivity field distribution diagram of the optimal position of the disinfection robot in the negative pressure isolation ward in Example 1. In the diagram, 1 represents the air supply vent, 2 represents the medical equipment belt, 3 represents the indoor airflow line, 4 represents the exhaust vent, 5 represents the hospital bed, 6 represents the sensitivity contour line, and 7 represents the optimal release position.

[0033] Figure 5 This is a schematic diagram of the flow field and the calculated optimal position of the irregularly shaped conference room in Example 2. In the diagram, 1 represents the air outlet, 2 represents the optimal release point, 3 represents the non-optimal release point, and 4 represents the round table area. Detailed Implementation

[0034] To enable those skilled in the art to better understand the present invention, the following detailed description, in conjunction with specific embodiments such as disinfection site deployment, fragrance release, localized cooling, air conditioning energy saving, extreme value deviation control, and emergency purification, further illustrates the present invention. The following embodiments are used to explain the technical solution of the present invention and do not limit the application of the present invention to scenarios such as anomaly source back-analysis, average air age analysis, thermal residence time analysis, or airflow dead zone testing.

[0035] Example 1: Optimal Position Optimization of Disinfection Robot (Based on "Maximizing Transport Efficiency")

[0036] This embodiment demonstrates how, when the airborne environmental factor is "disinfectant concentration," this invention can guide a mobile robot to find the most efficient docking and release point in a negative pressure environment with strict airflow control.

[0037] Scenario description: Select a standard negative pressure isolation ward. Figure 4 As shown, the negative pressure isolation ward includes an air supply vent 1 located at the top, a medical equipment belt 2 located on the wall, an indoor airflow 3 formed by the air supply vent 1, an exhaust vent 4 located at the bottom of the wall, and a hospital bed 5. Figure 4 The diagram also shows the sensitivity contour lines 6 calculated based on the adjoint equation, and the optimal release location 7 determined after feasible region screening. The optimization objective is to find an optimal docking location for targeted spraying, given the limited total amount of disinfectant carried by the robot, so as to maximize the cumulative disinfectant dose (CT value) received by the key disinfection areas (around the hospital bed and the medical staff's operating area), that is, to maximize the transport efficiency.

[0038] Step S1: Physical Modeling and Flow Field Calculation: Establish a three-dimensional geometric model of the ward, including the air inlet (1) and the air outlet (4). Solve the steady-state flow field. According to the general model described in claim 2, the physical quantity φ is the disinfectant concentration C. The effective transport and diffusion coefficient is set as follows: The turbulent Schmidt number Sc t The value of 0.9 was determined based on the characteristics of indoor low-speed turbulent environment and a large number of simulation verifications, and it can accurately simulate the corresponding physical transport behavior.

[0039] Step S2: Forward distribution field simulation. Solve the forward scalar transport equation in the time domain [0, T] to simulate the evolution of the concentration field after the hypothetical source is released.

[0040] Step S3: Construct the objective function and virtual source terms

[0041] 1. Target definition: The surface of the railing of the hospital bed (5), the area around the hospital bed, and the breathing area of ​​medical staff are set as the target areas.

[0042] 2. Objective Function Construction: Adopting the criterion of "maximizing transport efficiency," the objective function J1 is defined as the total cumulative amount of airborne environmental elements within the target area:

[0043]

[0044] 3. Construction of the dummy source term: Based on variational derivation, the dummy source term q of the adjoint equation is constructed. λ It is only related to spatial weights: q λ =w(x) The accompanying source terms in the target region are set to constants (such as 1), which means that "importance" starts to propagate backward from these regions.

[0045] Step S4: Reverse Solving of the Adjoint Equation. Using the frozen flow field data, the adjoint equation is solved in reverse time. The adjoint scalar (sensitivity information) diffuses backward from the exhaust vent (4) and the target area to the entire field, revealing the influence weight of each upstream point on the downstream target area.

[0046] Step S5: Sensitivity Field Generation and Feasible Region Screening

[0047] 1. Generate the original sensitivity field: obtain the full-field three-dimensional sensitivity distribution (6).

[0048] 2. Constructing a feasible region mask for the robot: Since the mobile robot can only travel on the ground and cannot collide with the hospital bed or cabinet, the system loads the ward map data to generate a two-dimensional feasible region mask (2D Mask). Extract the horizontal cross-sectional data of the robot nozzle height (e.g., 1.2m above the ground); force the sensitivity of the corresponding areas of the hospital bed (5), equipment belt (2), wall, etc. in the cross-section to zero.

[0049] 3. Optimization: Search for the point of maximum sensitivity within the planar region after masking.

[0050] 4. Results Analysis: The calculation results show that although the theoretical sensitivity of the upstream flow field (below the air inlet (1)) is very high, it is masked out because it is outside the travel path. The final determined optimal engineering location (7) is located in a specific vortex stagnation zone between the tail of the bed and the return air inlet. When released at this point, the disinfectant can be entrained by the local vortex and remain around the bed (5) for a long time, rather than being quickly sucked away by the exhaust vent (4).

[0051] Step S6: The robot's execution processor will calculate the coordinates (x... opt y opt It converts the command into a navigation command, autonomously navigates to the location, locks the brakes, and activates the spray mode, achieving the desired disinfection effect with minimal pesticide consumption.

[0052] Example 2: Optimal Position Optimization of Fragrance Diffuser (Based on "Optimized Distribution Uniformity")

[0053] This embodiment demonstrates how to use the method of the present invention to solve the problem of failure of traditional empirical point placement in complex geometric spaces.

[0054] Scenario description: such as Figure 5 As shown, an irregularly shaped conference room with an L-shaped corner structure is selected as the calculation object. This conference room includes an air vent 1, an optimal release point 2, a non-optimal release point 3, and a round table area 4. The round table area 4 is the target area in this embodiment. Due to the corner partition inside the conference room, the airflow from the air vent 1 is affected by the corner of the wall before entering the round table area 4, resulting in significant differences in the efficiency and uniformity of fragrance released from different spatial locations entering the target area. Therefore, the optimization objective of this embodiment is to determine the optimal release position of the fragrance source so that the fragrance can cover the round table area 4 quickly and evenly.

[0055] Step S1: Physical Modeling and Flow Field Calculation: Establish a three-dimensional geometric model of the conference room, including the L-shaped partition, air vents (1), and round table area (4), and divide the computational mesh. Solve the Reynolds-averaged Navier-Stokes (RANS) equations using the finite volume method (FVM), and in conjunction with the RNG turbulence model, obtain the steady-state velocity field u and turbulent viscosity field v under the condition that the indoor air conditioning is on. t According to the universal transport model proposed in this invention, when the object being processed is an airborne substance (fragrance), the scalar physical quantity φ corresponds to the concentration C, and the effective transport diffusion coefficient Γ... eff This corresponds to the effective diffusion coefficient D. eff Its definition remains unchanged:

[0056]

[0057] Among them, D mol The laminar diffusion coefficient of fragrance molecules (taken as 1.0 × 10⁻⁶). -5 m 2 / s), v t Sc is the turbulent kinematic viscosity calculated by the turbulence model. t Sc represents the turbulent Schmitt number. In the indoor low-speed turbulent environment of this embodiment, Sc t The value ranges from 0.7 to 0.9, to distinguish it from the Prandtl number in heat energy transfer.

[0058] Step S2: Forward Concentration Field Simulation: Based on the preset initial conditions (the overall concentration is 0 at the initial moment), solve the scalar transport equation in the time domain [0, T]. Obtain the concentration field distribution C(x, t) of the fragrance in the indoor space as it evolves over time.

[0059] Step S3: Accompanying settings:

[0060] 1. Target area definition: Select a cylindrical space with a height of 1.0m to 1.5m directly above the round table as the target area Ω. r .

[0061] 2. Objective Function Construction: Construct an objective function J2 to minimize the difference between the actual concentration C(x,t) and the spatial average concentration within the region. Distribution variance:

[0062]

[0063] Virtual source term construction: Based on the variational principle, construct the virtual source term q of the adjoint scalar transfer equation. λ Within the target region, the source term value is determined by the deviation of the local concentration from the spatial mean, i.e. In the adjoint equation, the source term value in the target region is set to the spatial concentration deviation value (a region above the average value generates a positive drive, and a region below the average value generates a negative drive), while the value in the remaining non-target regions is set to 0.

[0064] Step S4: Reverse Solution: Based on the frozen flow field data, solve the adjoint equation in reverse from t=300s to t=0s:

[0065]

[0066] The convective velocity is represented by -u, i.e., the accompanying scalar C. * It propagates against the direction of airflow "back to the source" to obtain sensitivity information on the uniformity of concentration distribution in the target area at all points in the field.

[0067] Step S5: Generate and optimize the sensitivity field: Based on the calculated full-field adjoint concentration field C * (x, t), generate a full-field sensitivity map. The system imports interior decoration drawing data and generates a space feasible region mask. The sensitivity of the interior of the wall, the interior of the furniture, and the area without power access is forced to zero. The maximum point is searched in the filtered sensitivity field. The calculation results show that the optimal release point (2) is not the intuitively thought center of the round table (4) or the innermost corner of the wall (3), but a specific suspended point (2) located below the side of the air conditioner vent.

[0068] Step S6: Result Output and Execution: The system will output the calculated three-dimensional coordinates (x, y, y) of the optimal sensitivity point. opt y opt , z opt The output is sent to the control terminal to guide engineers in installing the aroma diffuser at that coordinate.

[0069] Example 3: Precision cooling source location optimization in high-density server rack areas of data centers (based on "precise matching target value")

[0070] Scenario Description: A high-density data center with multiple rows of server racks is selected. Due to a surge in heat generation from some high-performance computing (HPC) racks, localized overheating has occurred. The optimal deployment location for newly installed "precision air vents" or "mobile point chillers" needs to be determined to precisely maintain the temperature at the air inlet of the faulty rack at the target value (e.g., 24°C). This aims to eliminate hotspots while avoiding excessive cooling and energy waste.

[0071] Step S1: Physical Modeling and Flow Field Calculation: Establish a 3D model including the cabinet, raised floor, and hot / cold aisle enclosed system. Solve for the steady-state flow field. According to the general model described in claim 2, the physical quantity φ is the air temperature T. Effective transport and diffusion coefficient Γ. eff This corresponds to the effective thermal diffusivity α. eff :

[0072]

[0073] Where α mol v is the thermal diffusivity of air molecules. t The viscosity is the turbulent viscosity. Specifically, in this embodiment, the turbulent Prandtl number Pr is... t The value is set to 0.85 to accurately characterize the heat transport characteristics in turbulent airflow.

[0074] Step S2: Forward distribution field simulation: Solve the forward energy (temperature) transport equation in the time domain to obtain the current temperature distribution field T(x, t).

[0075] Step S3: Construct the objective function and virtual source terms

[0076] 1. Target area definition: Set the front panel air intake area of ​​the overheated cabinet as the target area Ωr.

[0077] 2. Objective Function Construction: Using the "exact matching" criterion, an objective function is constructed to minimize the sum of squared deviations between the actual temperature and the ideal target temperature.

[0078]

[0079] Among them, T target The ideal target value is defined as follows. In this embodiment, the ideal target value can be taken as:

[0080] T tar (x, t) = T target =24℃

[0081] 3. Construction of the dummy source term: Based on the variational principle, the dummy source term q of the adjoint equation is constructed. λ Driven by temperature deviation:

[0082] q λ=2[T(x,t)-T tar (x, t)]

[0083] When the temperature at a certain point is higher than the target value, a positive accompanying source is generated; when it is lower than the target value, a negative accompanying source is generated. The accompanying equation propagates this "deviation signal" back to find the source of the deviation.

[0084] Step S4: Inverse solution of the adjoint equation: Using the frozen flow field data, solve the adjoint energy equation in reverse time. The full-field sensitivity field reveals: "Where to inject cold air can most effectively correct the temperature deviation in the target area."

[0085] Step S5: Feasible Domain Filtering and Optimization: The system loads the infrastructure drawings of the computer room and generates a strict feasible domain mask; eliminates all space occupied by cabinets, columns and cable trays; eliminates the central part of the main aisle (space for manual inspection and equipment handling needs to be reserved); only retains areas in the raised floor grid that can be replaced with perforated floor or where portable air conditioners can be placed.

[0086] Calculation results: The extreme sensitivity point after masking is located two floor tiles in front of the faulty cabinet, rather than directly in front as intuitively thought.

[0087] Mechanism: CFD flow field analysis shows that the cold airflow at this location can be directly drawn into the air inlet of the cabinet with minimal mixing loss by means of the vortex structure in the cold aisle, thereby achieving the most precise temperature control.

[0088] Step S6: Execution: The system outputs the optimal grid coordinates to guide maintenance personnel to replace the smart floor with a fan or deploy a mobile cooling unit at that location.

[0089] Example 4: Minimum Energy Consumption Temperature Control Optimization for Office Building HVAC (Based on "Minimizing Released Energy Consumption or Released Costs")

[0090] This embodiment demonstrates how, when the airborne environmental factor is air temperature, the present invention can be used to minimize air conditioning energy consumption while meeting the internal temperature standard, thus meeting the building energy conservation requirements.

[0091] Scenario Description: Select an open-plan office area (20m long, 15m wide, 3m high) containing employee workstations, a conference table, and office furniture. The optimization goal is to control the temperature in the workstation area (target area) to ≤26℃ (target threshold = 26℃), minimizing air conditioning energy consumption and reducing operation and maintenance costs while meeting employee comfort needs.

[0092] Step S1: Physical Modeling and Flow Field Calculation: Establish a 3D geometric model of the office area, including 4 air supply vents and 2 side return air vents, and recreate the layout of desks and workstations. Solve the steady-state flow field using the Reynolds-averaged Navier-Stokes (RANS) equations, and combine this with the RNG turbulence model to obtain the overall velocity vector u and turbulent viscosity v. t In this embodiment, the airborne environmental factor is temperature T, and the effective transport diffusion coefficient is the effective thermal diffusivity.

[0093]

[0094] The thermal diffusivity of air molecules α mol =2.0×10 -5 m 2 / s, Prandtl number for turbulence Pr t =0.85, accurately characterizing the turbulent heat transport properties.

[0095] Step S2: Forward distribution simulation: Based on the initial conditions (initial temperature of the entire field is 29℃, and the initial cooling capacity of the air conditioner is 1200W), the forward energy transfer equation is solved in the time domain [0,300s] to obtain the temperature distribution T(x,t) of the office area over time.

[0096] Step S3: Construct the objective function and virtual source terms

[0097] 1. Target area definition: Select a rectangular space with a height of 1.0 to 1.5 meters around the employee workstations as the target area Ω. r and the target area Ω r The spatial integration range serves as the temperature compliance penalty term; the space outside the target area is not included in the calculation of this compliance penalty term.

[0098] 2. Objective function construction: Set the target threshold φ lim =26℃, constraint weight μ=10 (prioritize temperature ≤26℃, then reduce energy consumption), source release energy consumption power P s (t) represents the instantaneous cooling output power of the air conditioner, and the objective function is:

[0099]

[0100] 3. Construction of Virtual Source Terms: Based on the adjoint principle, the virtual source terms of the adjoint equation are driven by compliance constraints, and their expression is:

[0101] q λ =20max(0, T(x, t) - 26)

[0102] The virtual source term is constructed according to the penalty form of "the difference between the target area compliance threshold and the scalar variable of the airborne environmental element" in the claims, driving the sensitivity field to propagate backward.

[0103] Step S4: Reverse solution of the adjoint equation: Using the turbulent field data calculated in step S1, reverse the solution of the adjoint energy transfer equation from t=300s to t=0s. The adjoint quantity (energy consumption optimization sensitivity information) diffuses backward from the target area, revealing where to place the air conditioning vents and at what intensity to release the cooling capacity, so as to save the most energy while meeting the standards.

[0104] Step S5: Sensitivity Field Generation and Two-Step Optimization

[0105] 1. Generate the original sensitivity field: obtain the three-dimensional energy consumption optimization sensitivity distribution of the office area. The high sensitivity area indicates that the location releases cold energy, with low energy consumption and easy to make the target area meet the standard;

[0106] 2. Construct a feasible area mask: Load the ceiling decoration drawings of the office area, generate a feasible area mask, remove the areas occupied by the ceiling joists, lighting fixtures, and fire protection facilities, and retain only the ceiling grid area where air supply outlets can be arranged;

[0107] 3. Select the optimal basic location: reuse the optimal air outlet location that maximizes the cumulative impact of claim 4 (the airflow convergence area on the ceiling near the workstation side, where the cooling capacity can quickly cover the target area and the basic energy consumption is low);

[0108] 4. Inverse calculation of minimum energy consumption: Based on the sensitivity field and objective function J, the minimum cold energy release intensity of the air outlet is calculated in reverse, and the result is 850W (30.8% lower than the initial intensity).

[0109] 5. Verification Results: Through forward simulation verification, with the release of 850W of cooling capacity, the temperature in the target area at this location is stable at 24.5~25.8℃ (meeting the ≤26℃ standard requirement), and the total energy consumption is reduced by 28.3% compared with the traditional layout, achieving the dual goals of meeting the standard and saving energy.

[0110] Step S6: The execution system outputs the optimal air outlet position (X=8.5m, Y=6.2m, Z=3.0m) and minimum cooling capacity release intensity (850W) to the air conditioning control system to guide the operation and maintenance personnel in adjusting the parameters and implementing the energy-saving optimization plan.

[0111] Example 5: Temperature Control Optimization for Minimum Extreme Deviation in Data Center Cabinet Area (Based on "Minimizing the Extreme Deviation of the Target Area")

[0112] This embodiment demonstrates how, when the airborne environmental factor is "air temperature," this invention can be used to eliminate extreme temperatures in the data center cabinet area, prevent local hotspots from causing server failures, and ensure stable equipment operation.

[0113] Scenario Description: A high-density data center rack area (containing 8 rows of racks, 6 racks per row) is selected. Some high-performance computer racks are experiencing a surge in heat generation, resulting in localized hotspots. The optimization goal is to control the extreme temperature deviation in the rack air intake area (target area), ensuring a maximum temperature ≤28℃ and a minimum temperature ≥20℃, eliminating the risk of localized overheating or undercooling, and preventing server failures.

[0114] Step S1: Physical Modeling and Flow Field Calculation: Establish a 3D geometric model of the cabinet area, including the raised floor (perforated air supply), hot and cold aisle enclosure system, cabinets, and exhaust vents. Solve the steady-state flow field using the RANS equations, with temperature T as the airborne environmental factor and the effective thermal diffusivity as follows:

[0115]

[0116] Prt = 0.85, which yields the total velocity vector and thermal diffusivity data.

[0117] Step S2: Forward distribution field simulation: Solve the forward energy transfer equation in the time domain [0, 400s] to simulate the temperature distribution field T(x, t) under the current air supply of the air conditioner. It was found that the local temperature at the air inlet of the faulty cabinet reached 31℃, which exceeded the upper limit of 28℃. The air inlet temperature of the adjacent cabinet was 19℃, which was lower than the lower limit of 20℃, and there was a significant extreme value deviation.

[0118] Step S3: Construct the objective function and virtual source terms

[0119] 1. Target area definition: Select a cuboid space within a height range of 0.5m to 1.0m from the air inlet of 8 rows of cabinets as the target area, and extract the instantaneous highest temperature and instantaneous lowest temperature within this target area to construct the maximum over-limit penalty item and the minimum under-limit penalty item;

[0120] 2. Objective function construction: Set an upper temperature limit φ u =28℃, lower limit φ l =20℃, time weight η(t) = 1.5 (weight increases during the steady-state phase t = 200~400s), objective function is:

[0121]

[0122] 3. Virtual source term construction: q λ =3max(0,T) max (t)-28)δ(xx max (t))-3max(0,20-T min (t))δ(xx min (t))

[0123] Where, x max(t) represents the spatial coordinates corresponding to the instantaneous highest temperature in the target area, x min (t) represents the spatial coordinates corresponding to the instantaneous lowest temperature in the target area. The source term focuses on the extreme point and drives the sensitivity field to find the optimal position to eliminate the extreme value in reverse.

[0124] Step S4: Inversely solve the adjoint equation. Based on the frozen flow field, solve the adjoint energy equation in reverse to obtain the global extreme value optimization sensitivity field. The high sensitivity region indicates that placing a cooling source at that location can eliminate the temperature extreme value the fastest.

[0125] Step S5: Sensitivity Field Generation and Two-Step Optimization

[0126] 1. Feasible area mask: Load the data center infrastructure drawings, eliminate the areas inside the cabinets, columns, cable trays and main passageways, and only retain the areas where the raised floor can be replaced with smart perforated floor;

[0127] 2. Select the optimal location based on the foundation: the optimal cooling location that maximizes the cumulative impact (the area of ​​the raised floor in front of the faulty cabinet);

[0128] 3. Inverse intensity calculation: Based on the sensitivity field, the emission intensity is calculated in reverse, the cold air output power is adjusted to 1500W, and the air delivery angle is finely adjusted at the same time;

[0129] 4. Verification Results: Forward simulation shows that the highest temperature in the target area dropped to 27.2℃ (≤28℃), the lowest temperature rose to 20.8℃ (≥20℃), the extreme value deviation decreased from 12℃ to 6.4℃, eliminating the potential for local hot or cold spots, and the server operated stably.

[0130] Step S6: The system outputs the optimal location of the smart floor and the intensity of the cold air release, guiding maintenance personnel to replace the smart perforated floor at the corresponding location, and after adjusting the parameters, implement the extreme value elimination solution.

[0131] Example 6: Optimization of Rapid Formaldehyde Emergency Purification in Laboratories to Achieve Standards (Based on "Reaching Stable Standards as Quickly as Possible")

[0132] This embodiment demonstrates how, when the airborne environmental factor is "pollutant concentration," the present invention can be used to quickly locate the release point of the purification agent, enabling the formaldehyde concentration in the laboratory to rapidly reach a stable and compliant state, thus adapting to emergency purification scenarios.

[0133] Scenario Description: After the laboratory was newly renovated, the formaldehyde concentration exceeded the standard (initial concentration 0.25 mg / m³). 3 National standard φ std =0.08mg / m 3 The objective is to rapidly release purifying agents to decompose formaldehyde, with the goal of quickly achieving and stabilizing the formaldehyde concentration in the laboratory work area (target area) at 0.08 mg / m³. 3The following measures will shorten the laboratory's start-up time.

[0134] Step S1: Physical Modeling and Flow Field Calculation: Establish a three-dimensional geometric model of the laboratory, including one air inlet, one air outlet, an experimental table, and a fume hood. Solve for the steady-state flow field, with the airborne environmental factor being the formaldehyde concentration C, and the effective mass diffusion coefficient being:

[0135]

[0136] Formaldehyde molecular diffusion coefficient D mol =1.5×10 -5 m 2 / s, turbulent Schmidt number Sc t =0.8, characterizing the turbulent diffusion properties of formaldehyde.

[0137] Step S2: Forward distribution field simulation. Solving the forward concentration transport equation in the time domain [0, 360s] simulates the evolution of formaldehyde concentration under current conditions without purification. It was found that it takes 320s for the formaldehyde concentration in the target area to drop to 0.08 mg / m³. 3 Furthermore, the results fluctuate significantly after the target is met.

[0138] Step S3: Construct the objective function and virtual source terms

[0139] 1. Target area definition: A rectangular space (work area) with a height of 1.0 to 1.5m on the laboratory bench;

[0140] 2. Objective function construction: Set the target value φ s =0.08mg / m 3 The stability deviation weight β = 0.5, and the objective function is:

[0141]

[0142] 3. Construction of virtual source terms:

[0143] q λ =δ(tt) s )+2×0.5[C(x,t)-0.08]H(tt) s )

[0144] Among them, H(tt) s ) is the Heaviside function. This virtual source term is used to drive the sensitivity field to inversely find the "fastest and most stable optimal position".

[0145] Step S4: Reverse solution of the adjoint equation: Based on the frozen flow field, reverse solution of the adjoint concentration transport equation is performed from t=360s. The adjoint scalar focuses on the "rapid mass transfer path", and the high-sensitivity region is the position where "formaldehyde can decompose and reach the standard the fastest after the release of the purification agent".

[0146] Step S5: Sensitivity Field Generation and Optimization:

[0147] 1. Feasible area mask: Eliminate the areas of the laboratory bench, fume hood, walls, and personnel passage, and retain only the floor area where mobile purification equipment can be placed;

[0148] 2. Optimal location selection: Based on the sensitivity field, a high-sensitivity location (below the side of the laboratory air inlet, X=3.2m, Y=4.0m, Z=0.5m) is selected where the airflow can directly reach the target area without eddy current stagnation. At this location, the purification agent can quickly diffuse to the target area with the airflow, resulting in the highest mass transfer efficiency.

[0149] 3. Inverse calculation of release intensity: The release intensity of the purification agent was determined by inverse calculation based on the sensitivity field and was set at 0.8 g / s;

[0150] 4. Verification Results: Forward simulation shows that, at this location with a release rate of 0.8 g / s, the formaldehyde concentration in the target area can be reduced to 0.075 mg / m³ in just 180 seconds. 3 Furthermore, after meeting the standard, the fluctuation range is ≤±3%, and the time to achieve stable compliance is shortened by 43.7% compared to traditional locations.

[0151] Step S6: Execution: The system outputs the optimal location and release intensity of the purification equipment, guiding staff to deploy mobile purification equipment, quickly complete the emergency purification of formaldehyde in the laboratory, and enable the laboratory to be put into use ahead of schedule.

Claims

1. A computer-executed method for optimizing the location of indoor airborne environmental elements based on adjoint equations, characterized in that, Includes the following steps: Step S1: Construct a physical model of the indoor space, solve the flow field of indoor air flow, and obtain the full-field velocity vector data and effective transmission diffusion coefficient data; Step S2: Based on the set initial conditions, solve the forward scalar transport equation in the time domain [0, T] to obtain the forward distribution field of indoor airborne environmental elements as a function of time; the airborne environmental elements include airborne substance concentration, air temperature or air enthalpy. Step S3: Based on the specific optimization task requirements, construct an objective function J that reflects the control performance index of the indoor target area; based on the variational principle, use the Fréchet derivative of the objective function with respect to the scalar variables of the airborne environmental elements to construct a virtual source term for the accompanying scalar transport equation. Step S4: In the time domain [0, T], using the velocity vector data and effective transmission diffusion coefficient data, and driven by the virtual source term, solve the accompanying scalar transmission equation in reverse time to obtain the full-field accompanying scalar field; Step S5: Map the entire field of the accompanying scalar field to generate a sensitivity field. The sensitivity value at any location in space is determined by the accompanying scalar value corresponding to that location. The sensitivity field is filtered using a preset feasible region mask, and the spatial coordinates that make the objective function reach an extreme value are selected from the filtered sensitivity field as the target spatial location of the airborne environmental element source.

2. The method according to claim 1, characterized in that, The general form of the scalar transport equation in steps S2 and S4 is: Forward equation: Adjoint equation: Where φ is a scalar physical quantity of the airborne environmental element, λ is an accompanying scalar, u is a velocity vector, and Γ is a velocity vector. eff For the effective transport diffusion coefficient, S φ q represents the source term intensity of airborne environmental factors. λ The virtual source term of the adjoint equation is constructed from the objective function; the effective transport diffusion coefficient is a spatial distribution function constructed based on the superposition of the turbulent motion characteristics of the flow field and the molecular diffusion characteristics of environmental elements.

3. The method according to claim 2, characterized in that, When the airborne environmental element is an airborne substance, the physical quantity φ is the concentration C, and the effective transport diffusion coefficient Γ is... eff The effective mass diffusion coefficient D eff And satisfy: Where D mol v is the molecular mass diffusion coefficient. t For turbulent kinematic viscosity, Sc t For turbulent Schmidt number; When the airborne environmental element is thermal energy, the physical quantity φ is the temperature T or the air enthalpy h, and the effective transport diffusion coefficient Γ is... eff The effective thermal diffusivity α eff And satisfy: Where α mol Pr is the thermal diffusivity of air molecules. t For turbulent Prandtl number.

4. The method according to claim 1, characterized in that, The objective function J is defined as the total cumulative amount of airborne environmental factors within the target area: Where Ω is the computational domain, w(x) is the spatial weight function, and w(x) takes a non-zero constant value within the preset target region and a value of 0 outside the target region; the corresponding virtual source term is expressed as: q λ =w(x) In step S5, the spatial coordinates corresponding to the point with the maximum value in the filtered sensitivity field are selected as the optimal source location.

5. The method according to claim 1, characterized in that, The objective function J in step S3 is defined as the distribution variance of airborne environmental elements within the target area: Among them, Ω r For the target area, The spatial average value of airborne environmental elements within the target area at time t; the corresponding adjoint equation virtual source term is: In step S5, the point in the filtered sensitivity field that minimizes the objective function is selected as the target spatial location of the airborne environmental element source.

6. The method according to claim 1, characterized in that, The objective function in step S3 is defined as the sum of squared deviations between the calculated value and the ideal objective value: Where, φ tar (x, t) represents the ideal objective value; the corresponding adjoint equation dummy source term is: q λ =2[φ(x,t)-φ tar (x,t)] In step S5, the point in the filtered sensitivity field that minimizes the objective function is selected as the target spatial location of the airborne environmental element source.

7. The method according to claim 1, characterized in that, The objective function in step S3 is defined as the weighted sum of the total energy consumption or total energy released from the source and the penalty term for achieving the target area: Among them, P s (t) represents the instantaneous release intensity or energy consumption power of the source, φ lim The threshold value for the target region is μ, where μ is the constraint weight; the corresponding adjoint equation virtual source term is... q λ =2μmax(0,φ(x,t)-φ lim ) In step S5, the maximum total accumulation of airborne environmental elements within the target area is first used as an auxiliary objective to solve for the corresponding spatial coordinates as the basic position. Then, the minimum release intensity or minimum energy consumption is solved in reverse based on the sensitivity field and the objective function. If the basic position cannot make the objective function converge to the set threshold, the point that minimizes the objective function is reselected in the filtered sensitivity field as the target spatial position of the airborne environmental element source.

8. The method according to claim 1, characterized in that, The objective function in step S3 is defined as the weighted sum of the maximum exceedance penalty and the minimum under-limit penalty for airborne environmental elements within the target area: Where, φ max (t) represents the instantaneous maximum physical quantity of the target region, φ min (t) represents the instantaneous minimum physical quantity of the target region, φ u φ1 is the upper limit threshold of the physical quantity, φ2 is the lower limit threshold of the physical quantity, and η(t) is the time weight; the corresponding adjoint equation virtual source term is: q λ =2η(t)max(0,φ max (t)-φ u )δ(xx max (t))-2η(t)max(0,φ1-φ min (t))δ(xx min (t)) Where, x max (t) represents the spatial coordinates corresponding to the instantaneous maximum physical quantity in the target region, x min (t) represents the spatial coordinates corresponding to the instantaneous minimum physical quantity in the target region, δ(xx) min (t) is the Dirac function; In step S5, the total cumulative amount of airborne environmental elements in the target area is maximized as an auxiliary objective, and the corresponding spatial coordinates are solved as the basic position. Then, the release intensity is calculated in reverse based on the sensitivity field. If the basic position cannot eliminate the extreme value hazard, the point that minimizes the objective function is reselected in the filtered sensitivity field as the target spatial position of the airborne environmental element source.

9. The method according to claim 1, characterized in that, The objective function in step S3 is defined as the weighted sum of the achievement time penalty term and the stability deviation penalty term: Among them, t s The time it takes for the target region to first reach and stabilize at the standard value, β is the stability deviation weight, and φ is the value of the standard deviation. s The target region's stable compliance standard value; the corresponding adjoint equation virtual source term is: q λ =δ(tt s )+2β[φ(x,t)-φ s ]H(tt s ) Among them, H(tt) s ) is the Heaviside function. In step S5, the maximum point in the mainstream airflow region or the efficient transmission region without backflow eddy stagnation is selected as the optimal source location based on the sensitivity field, and then the release intensity is calculated in reverse based on the sensitivity field.

10. The method according to claim 1, characterized in that, The feasible domain mask is a two-dimensional or three-dimensional Boolean matrix that corresponds one-to-one with the computational domain grid. The region where airborne environmental element sources can be arranged is assigned a value of 1, and the region where airborne environmental element sources cannot be arranged is assigned a value of 0. The sensitivity field is: G(x,t)=|λ(x,t)| The sensitivity field is filtered using the feasible region mask to obtain the filtered sensitivity field: G m (x,t)=M(x)G(x,t) Where G(x,t) is the sensitivity field before filtering, G m (x, t) is the filtered sensitivity field, and M(x) is the feasible region mask; the target spatial location of the airborne environmental element source includes the actual source location for releasing airborne substances, heat or cold, or the virtual release source location for characterizing the abnormal source of the airborne environmental element; when the airborne environmental element source is a virtual release source, the spatial location where the abnormality of the airborne environmental element is detected is set as the target area, and the detection value is associated with the virtual source term of the adjoint equation, and the sensitivity field is used to characterize the probability field of the existence of the virtual release source; The target spatial location also includes test locations used to characterize the average air age, thermal residence time, or airflow dead zone of the entire field or a local area.

Images