A building energy flexibility potential assessment method based on semi-supervised load decomposition

Abstract

The application discloses a building energy flexibility potential evaluation method based on semi-supervised load decomposition, first, the total load data, environmental data, indoor thermal comfort state data, region type label and temperature-sensitive load label data of a plurality of regions of a plurality of floors of a target building are acquired, and data preprocessing is performed; a semi-supervised contrast regression learning model is constructed, the total load data and environmental data are taken as input, and the total load time sequence representation is extracted through self-supervised contrast learning; then, a physical mechanism constrained data-driven thermal comfort response model is constructed and trained, finally, the benchmark temperature-sensitive load sequence is acquired to calculate the benchmark temperature-sensitive load energy consumption, and the optimized temperature-sensitive load energy consumption is acquired through the physical mechanism constrained data-driven thermal comfort response model, the benchmark temperature-sensitive load energy consumption and the optimized temperature-sensitive load energy consumption are summed respectively, and the energy flexibility potential rate is calculated. The method can accurately evaluate the building energy flexibility potential under limited measurement conditions.

Description

Technical Field

[0001] This invention relates to the field of building energy management technology, specifically a method for assessing the building energy flexibility potential based on semi-supervised load decomposition. Background Technology

[0002] Loads in buildings that change with external weather conditions and indoor temperature setpoints, such as heating, ventilation, air conditioning, and heat pump system loads, are generally referred to as temperature-sensitive (TS) loads. TS loads are among the energy consumers in buildings with relatively strong energy-saving capabilities. By adjusting indoor temperature setpoints, pre-cooling, pre-heating, or load reduction, energy consumption can be reduced or electricity demand shifted while still meeting the thermal comfort needs of residents. As the proportion of renewable energy in the power grid continues to increase, the importance of buildings as demand-side flexible resources is becoming increasingly prominent. Accurately assessing the energy flexibility potential of building temperature-sensitive loads is crucial for building energy management, demand response, and energy-saving dispatch.

[0003] However, in actual buildings, due to limitations in sensor installation costs, retrofitting difficulties, wiring conditions, and operation and maintenance costs, building management systems often only possess total load metering data for each area or circuit, lacking individual metering data for temperature-sensitive loads in all areas. If it is directly assumed that the temperature-sensitive loads in each area are fully measurable, the energy flexibility potential assessment results often lack reliable support in engineering applications.

[0004] Existing load decomposition methods have the following shortcomings: On the one hand, existing semi-supervised load decomposition methods often treat different areas on different floors as independent samples. However, for multi-story, multi-area buildings, areas with the same function or similar spatial structure on different floors usually have similar occupancy patterns, equipment configurations, building envelope conditions, and load composition characteristics. Existing methods do not fully utilize the prior knowledge of spatial structure across floors or areas, resulting in insufficient decomposition accuracy under conditions with a small number of temperature-sensitive load labels, making it difficult to effectively transfer the decomposition knowledge of measured areas to unmeasured areas.

[0005] On the other hand, contrastive learning of time series can improve representation learning capabilities in scenarios where labels are scarce. However, the total building load sequence usually changes relatively smoothly, and conventional enhancement methods such as global jitter, scaling, or random masking can easily disrupt the original temporal structure or be easily recovered by the model through adjacent time points, thus limiting the gains of contrastive learning for load decomposition tasks.

[0006] Furthermore, there is a challenge in thermal comfort modeling that it is difficult to balance physical consistency with nonlinear expressive power. When implementing building energy flexibility measures, indoor thermal comfort constraints must be considered. Traditional physical thermal models (such as RC thermal models) have good interpretability and physical consistency, and can reflect building thermal inertia, but they are difficult to fully characterize the complex nonlinear relationships brought about by actual building operating conditions, human behavior, and equipment control. Pure data-driven models, while having strong nonlinear fitting capabilities, lack thermodynamic mechanism constraints and are prone to overfitting or physically unreliable predictions under unfamiliar control scenarios, reducing the reliability of flexibility potential assessment.

[0007] In summary, under the condition of incomplete temperature-sensitive load metering, how to achieve accurate decomposition of temperature-sensitive loads by utilizing the similarity of spatial structures across floors, how to establish an accurate thermal comfort response model while maintaining physical consistency, and how to achieve building-level energy flexibility potential assessment based on this are technical problems that urgently need to be solved in this field. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of existing technologies and propose a building energy flexibility potential assessment method based on semi-supervised load decomposition. This method addresses the problems of incomplete temperature-sensitive load measurement, insufficient utilization of spatial similarity across floors, lack of physical consistency in purely data-driven thermal comfort models, and reliance on complete temperature-sensitive load measurement data for energy flexibility potential assessment. By using a semi-supervised contrastive regression learning model to decompose temperature-sensitive loads from the total load of unmeasured temperature-sensitive load areas, and by establishing a dynamic mapping between temperature-sensitive loads and indoor thermal comfort states through a data-driven thermal comfort response model constrained by physical mechanisms, the method optimizes the temperature-sensitive load sequence within an adjusted thermal comfort allowable range, thereby assessing the building's energy flexibility potential under limited measurement conditions.

[0009] To achieve the above objectives, the technical solution specifically adopted by the present invention is as follows: A method for assessing the building energy flexibility potential based on semi-supervised load decomposition includes the following steps: Step 1: Obtain the total load data, environmental data, indoor thermal comfort status data, area type labels, and temperature-sensitive load label data for several floors and areas of the target building, and perform data preprocessing; the area type labels are used to characterize the similarity of different areas in terms of function, spatial location, floor layout, room number, area, orientation, building envelope conditions, and equipment configuration; the indoor thermal comfort status data includes indoor temperature. Step 2: Construct a semi-supervised contrastive regression learning model. Using regional total load data and environmental data as input, extract the time series representation of total load through self-supervised contrastive learning. Utilize temperature-sensitive load label data of several floor areas and combine it with area type labels for semi-supervised regression training. By utilizing the spatial structural similarity between areas with the same area type label on different floors, the temperature-sensitive load is decomposed from the total load data of floor areas with unmeasured temperature-sensitive load. Step 3: Construct and train a data-driven thermal comfort response model constrained by physical mechanisms. The data-driven thermal comfort response model constrained by physical mechanisms includes a physical thermal model branch and a data-driven residual branch. Step 4: Use the temperature-sensitive load power sequence of each region as the benchmark temperature-sensitive load sequence, set the allowable range for indoor thermal comfort, and use the data-driven thermal comfort response model constrained by physical mechanisms to obtain the predicted sequence of indoor thermal comfort state within the control period. Under the condition that the predicted sequence of indoor thermal comfort state meets the allowable range for indoor thermal comfort, with the goal of minimizing the energy consumption of temperature-sensitive loads within the control period, obtain the optimized temperature-sensitive load power sequence; then, sum the energy consumption of the benchmark temperature-sensitive load and the optimized temperature-sensitive load respectively to calculate the energy flexibility potential rate.

[0010] Preferably, in step 2, the semi-supervised contrastive regression learning model includes a data augmentation module, an encoder, a self-supervised decoder, a regression decoder, and a discriminator; wherein, the data augmentation module is used to generate different augmented views of the input sequence, the encoder is used to extract time series representations, the self-supervised decoder is used to reconstruct the total regional load sequence, the regression decoder is used to output the temperature-sensitive load decomposition result, and the discriminator is used to adaptively select the sequence segments to be augmented in the next round of training based on the reconstruction error.

[0011] Preferably, the data amplification module employs a segmented amplification strategy: the input sequence is divided into several sequence segments according to a preset segment length, and one or more sequence segments are selected for local amplification; the local amplification includes segmented dithering amplification and segmented masking amplification. The segmented jitter amplification is defined as follows: in, Indicates that it follows the mean. variance is Gaussian noise, This is the Gaussian noise scaling factor. Represents the input sequence, where , Indicates length is The A sequence segment, and They represent respectively to The sequence segments obtained after segmented jitter amplification and segmented mask amplification; The segmented mask augmentation is defined as follows: .

[0012] Preferably, the self-supervised contrastive learning employs a self-supervised loss function. , represented as: in, and They represent the first The time step Original and reconstructed values ​​of each feature This indicates the batch size during model training. This represents the number of time steps in the input sequence. This represents the number of features at each time step. , and These represent the sample, time step, and feature index, respectively. and These represent the characterization sequences obtained after the two amplified views are encoded, where... and Indicates the first The sample at the th The representation vector corresponding to each time step This is an indicator function that takes the value 1 when the condition within the parentheses is true, and 0 otherwise. This represents the mean square reconstruction error. Will As positive sample pairs, they are compared with the representations of other time steps in the same sample; Then the characteristics of the same positive sample pairs are compared with those of other samples in the same batch.

[0013] Preferably, the adaptive amplification segment selection of the discriminator includes: calculating the absolute difference between the amplified sequence and the reconstructed sequence output by the self-supervised decoder. For each absolute difference The sequence execution kernel size is Max pooling operation; calculate the error of each sequence segment according to the preset segmentation method; select the segment with the largest error. Each sequence segment is used as a candidate segment for amplification in the next training iteration.

[0014] Preferably, in step 2, the semi-supervised regression training uses a multi-label perceptual contrastive loss function, the expression of which is as follows: in, Indicates calculation and Cosine similarity; This represents a nonlinear transformation used to map the temporal representation of the encoder output to a contrastive feature space; and This represents the representation obtained by the encoder. and These represent the positive sample set and the negative sample set, respectively, as defined by the region type label; This is used to maximize the similarity between samples of the same region type while minimizing the similarity between samples of different region types. and These represent the actual temperature-sensitive load and the temperature-sensitive load obtained from decomposition, respectively.

[0015] Preferably, in step 2, the training process of the semi-supervised contrastive regression learning model includes: the loss function used in the self-supervised pre-training stage is... Temporal representation learning is performed using total regional load data and environmental data from all areas of all floors of the building. The loss function used in the semi-supervised regression training phase is... The model utilizes temperature-sensitive load labeled data from a floor area and trains on a regression decoder based on the total load time series representation extracted by the encoder to effectively learn the mapping relationship between temperature-sensitive load and total load. In the practical application stage, the total load data and environmental data from areas where temperature-sensitive load is not measured are input into the trained model, and the corresponding temperature-sensitive load decomposition results are output.

[0016] Preferably, the training method for the data-driven thermal comfort response model constrained by the physical mechanism in step 3 is as follows: A data-driven thermal comfort response model constrained by physical mechanisms is trained using historical temperature-sensitive load power sequences, historical environmental data, and corresponding measured indoor thermal comfort state sequences. A physical reference response reflecting building thermal inertia is generated using the physical thermal model, and the residual between the measured indoor thermal comfort state and the physical reference response is used as the training objective for nonlinear correction of the data-driven model. This results in a data-driven thermal comfort response model constrained by physical mechanisms that can predict the indoor thermal comfort state sequence within a control period based on candidate temperature-sensitive load power sequences, corresponding environmental data, and the indoor thermal comfort state at the start of control.

[0017] Preferably, the method for obtaining the indoor thermal comfort state prediction sequence is as follows: the physical thermal model branch is a 3R2C physical model, which can output the physical reference indoor temperature sequence within the control period. The data-driven residual branch will incorporate historical temperature-sensitive loads. and historical environmental data The training input used for the data-driven residual branch is obtained through... Construct historical residual sequence data, where For historical real indoor temperature series data, The target value is used as the training value for the data-driven residual branch, and the data-driven residual branch is trained accordingly; in the prediction phase, the candidate temperature-sensitive load power sequence within the control period is used. and corresponding environmental data Input the trained data to drive the residual branch, according to Output residual prediction sequence ,in This represents the residual prediction mapping function composed of recurrent neural networks, long short-term memory networks, gated recurrent unit networks, bidirectional gated recurrent unit networks, temporal convolutional networks, or Transformer temporal networks. Indicates the network parameters obtained through training; and according to Obtain the indoor thermal comfort state prediction sequence .

[0018] Preferably, the physical thermal model is a 3R2C physical model, and its governing equations are: in, This indicates the indoor air temperature, i.e., the physical reference indoor temperature. Indicates the wall temperature. Indicates outdoor air temperature; , and These represent the thermal resistance between indoor air and the wall, between indoor air and outdoor air, and between the wall and outdoor air, respectively. and These represent the heat capacity of indoor air and walls, respectively. The formula for calculating the heat power acting on the building's thermal process after conversion from temperature-sensitive load is as follows: ,in, This represents the performance coefficient of temperature-sensitive load equipment. Used to indicate the direction of heating or cooling; it is set to 1 for heating and -1 for cooling. Represents discrete time points within the control cycle. Indicates the next adjustment time point within the adjustment cycle. This indicates the time interval between adjacent control points.

[0019] Preferably, the allowable range for indoor thermal comfort in step 4 is determined as follows: During the cooling season, the upper limit of the baseline indoor temperature is increased by the preset indoor temperature setting value; during the heating season, the lower limit of the baseline indoor temperature is decreased by the preset indoor temperature setting value; the predicted values ​​of indoor thermal comfort at each time point within the control cycle satisfy the following: ,in , These are the adjusted lower and upper limits for indoor thermal comfort, respectively.

[0020] Preferably, in step 4, the candidate temperature-sensitive load power sequences of each region within the control period are used as optimization variables. One or more of the following methods are employed: genetic algorithm, particle swarm optimization, Bayesian optimization, dynamic programming, or model predictive control. Under the condition that the indoor temperature prediction sequence corresponding to the candidate temperature-sensitive load power sequence meets the allowable range for indoor thermal comfort, the energy consumption of the temperature-sensitive load is solved. Minimum optimized temperature-sensitive load power sequence The optimization objective is expressed as: in, To optimize the power of candidate temperature-sensitive loads during the process, The time interval between adjacent control points. This represents the total number of time points within the control period.

[0021] Preferably, in step 4, the energy flexibility potential is characterized by the energy flexibility potential rate; The baseline temperature-sensitive load energy consumption and the optimized temperature-sensitive load energy consumption for each region are calculated as follows: No. The energy flexibility potential rate for each region is calculated as follows: No. The energy flexibility potential rate of each floor is calculated as follows: The energy flexibility potential of the entire building is calculated as follows: in, The first decomposition obtained in step 2 The region in the first Reference temperature-sensitive load power at each time point For the first The region in the first Optimized power of temperature-sensitive load at each time point The time interval between adjacent time points. This represents the total number of time points within the control period. For the first The set of areas contained in each floor The set of all areas encompassed by the target building. , and These are the energy flexibility potential rates at the regional, floor, and whole building levels, respectively.

[0022] Preferably, the environmental data includes one or more of the following: outdoor temperature, outdoor humidity, solar radiation, time characteristics, weekday characteristics, weekday identifiers, and holiday identifiers; the temperature-sensitive load includes one or more of the following: heating, ventilation, air conditioning, or heat pump system loads that vary with external meteorological conditions or indoor temperature setpoints. This invention has the following characteristics and beneficial effects: This invention employs a segmented amplification strategy within the SCRF framework. The input sequence is divided into several segments according to a preset segment length, and one or more segments are selected for local amplification (segmented dithering or segmented masking), rather than performing global amplification on the entire sequence. Compared to conventional global dithering, scaling, or random masking methods, segmented amplification can preserve the overall slowly varying temporal structure of the building load while selectively perturbing local peak segments, variable segments, or segments with large reconstruction errors. This avoids the problem of global enhancement damaging temporal characteristics or random masking being directly recovered by adjacent time points, thereby improving the self-supervised contrastive learning's ability to represent load decomposition tasks. This effect can be directly derived from the definition of segmented amplification (amplifying only a portion of the sequence segments while leaving the rest unchanged).

[0023] This invention introduces a discriminator into the SCRF framework to calculate the error between the amplified sequence and the encoder's reconstructed sequence. It statistically analyzes the error index of each sequence segment according to a preset segmentation method and selects one or more sequence segments with larger error indices as amplification candidate segments for the next round of training. This adaptive selection mechanism enables the encoder to automatically focus on load variation segments with poor reconstruction results and insufficient representation during training, thereby accelerating model convergence and improving the quality of temporal representation. This effect directly stems from the closed-loop training mechanism of "selecting amplified segments based on reconstruction error feedback."

[0024] This invention proposes a Multi-Label Perceptual Contrast Loss (MLA Loss). Based on region type labels, positive and negative sample pairs are constructed. Samples with the same region type label or similarity meeting a preset threshold are designated as positive samples, while samples with different region type labels or similarity below the preset threshold are designated as negative samples. This loss function optimizes the model by narrowing the representational distance between positive and negative samples and incorporating temperature-sensitive load prediction errors. This allows the model to fully utilize prior spatial structures across floors or regions, transferring the knowledge of temperature-sensitive load decomposition from a measured area on a single floor to other structurally similar but unmeasured floors, significantly improving decomposition accuracy even under conditions of scarce temperature-sensitive load labels. This effect directly stems from the way the Multi-Label Perceptual Contrast Loss utilizes region type labels and its joint optimization mechanism with regression loss.

[0025] This invention constructs a data-driven thermal comfort response model constrained by physical mechanisms, employing a residual structure that couples a physical thermal model with a data-driven residual branch. The physical thermal model generates a physical reference indoor temperature conforming to thermodynamic laws based on outdoor environmental variables and temperature-sensitive loads. The data-driven residual branch performs nonlinear correction on the deviation between the physical reference and measured values ​​based on temperature-sensitive loads, environmental data, and historical residual information. Finally, the physical reference output is superimposed with the residual prediction value to obtain the predicted value of the thermal comfort state. This structure enables the thermal comfort response model to possess both physical consistency and nonlinear expressive capability, maintaining a thermodynamically feasible prediction trajectory even under unfamiliar control scenarios, reducing the risk of overfitting or physically unreliable predictions in purely data-driven models. This effect directly stems from the coupled structural design of "physical reference + data-driven residual".

[0026] This invention organically combines temperature-sensitive load decomposition, thermal comfort response modeling, and temperature-sensitive load optimization under thermal comfort constraints: the SCRF model outputs the temperature-sensitive load decomposition results for unmeasured areas; the thermal comfort response model establishes a dynamic mapping relationship between temperature-sensitive loads and indoor thermal comfort states; and the optimization module solves for the optimal temperature-sensitive load sequence under the adjusted indoor thermal comfort allowable range constraints, aiming to reduce temperature-sensitive load energy consumption or operating costs, and assesses energy flexibility potential based on the difference in temperature-sensitive load energy consumption before and after optimization. Specific information transmission and coupling relationships exist between these modules (the temperature-sensitive load output by SCRF directly serves as the input excitation for the thermal comfort model, and the temperature prediction output by the thermal comfort model is used to constrain the optimization process), forming a complete "decomposition-modeling-optimization-evaluation" technical chain. This allows for the output of regional, floor-level, and building-wide energy flexibility potential under engineering conditions with only a small number of temperature-sensitive load metering devices, reducing reliance on temperature-sensitive load metering devices across the entire area and providing a reliable basis for building energy-saving scheduling and demand response decisions. This effect directly stems from the information coupling relationship between the modules and the complete technical chain they form; the absence of any module would prevent flexibility potential assessment under conditions of scarce labels. Attached Figure Description

[0027] Figure 1 This is an overall flowchart of a building energy flexibility potential assessment method based on semi-supervised load decomposition, according to an embodiment of the present invention.

[0028] Figure 2 This is a structural diagram of a semi-supervised contrastive regression learning model in an embodiment of the present invention.

[0029] Figure 3 This is a schematic diagram of the segmented amplification strategy in an embodiment of the present invention.

[0030] Figure 4 This is a schematic diagram illustrating the working principle of multi-label perception contrast loss in an embodiment of the present invention.

[0031] Figure 5 This is a flowchart of SCRF training and application in an embodiment of the present invention.

[0032] Figure 6 This is a structural diagram of the 3R2C physical thermal model in an embodiment of the present invention.

[0033] Figure 7 This is a structural diagram of a data-driven thermal comfort response model constrained by physical mechanisms in an embodiment of the present invention.

[0034] Figure 8 This is a comparison diagram before and after temperature-sensitive load optimization in an embodiment of the present invention. Detailed Implementation

[0035] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0036] A method for assessing the building energy flexibility potential based on semi-supervised load decomposition, such as Figure 1 As shown, the process includes four main steps: data acquisition, temperature-sensitive load decomposition, thermal comfort response modeling, and energy flexibility potential assessment.

[0037] Step 1: Data Acquisition and Organization: Acquire total load data, environmental data, indoor thermal comfort status data, single-floor data with temperature-sensitive load labels, and area type labels for all floors and areas of the target building, and perform data preprocessing. The area type labels are used to characterize the similarity of different areas in terms of function, spatial location, floor layout, room number, area, orientation, building envelope conditions, and equipment configuration. Total load data can be obtained from a building energy management system, smart meters, or sub-metering systems. Environmental data may include outdoor temperature, outdoor humidity, solar radiation, time characteristics, weekday characteristics, and weekday or holiday indicators. Indoor thermal comfort status data is preferably indoor temperature, but may also include indoor humidity or comfort indicators characterized by both temperature and humidity.

[0038] This embodiment focuses on a multi-story building. The building has temperature-sensitive load metering devices installed on only one or a few floors, while the remaining floors only have regional total load metering data. The floors have similar or partially similar room layouts, and rooms with the same number or function on different floors have similar load composition characteristics. The objective is to evaluate the energy flexibility potential of the target building under different indoor temperature setpoint adjustment strategies, given incomplete temperature-sensitive load labeling.

[0039] This embodiment uses the CU-BEMS real-world building dataset to describe the implementation steps of the method and verify its effectiveness. The CU-BEMS dataset was collected from data of some rooms on floors 3 to 7 of a building in Bangkok, Thailand. Floor 3 can be selected as the labeled floor, and floors 4 to 7 as unlabeled floors.

[0040] Furthermore, the dataset centrally obtains the total load power of the region, outdoor temperature, outdoor humidity, indoor temperature, and temperature-sensitive load power of some areas. If the environmental data comes from a weather station, the weather station data and building load data are aligned with a uniform time step. Data preprocessing includes missing value imputation, outlier removal, timestamp alignment, feature normalization, and sliding window construction. In a preferred embodiment, the sampling interval is 15 minutes, and the input window length T is set to 96, i.e., using data from the past 24 hours as an input sequence. Input features include regional total load, outdoor temperature, outdoor humidity, time features, and weekday identifiers. The reconstruction target in the self-supervised training phase is the regional total load sequence, and the prediction target in the semi-supervised regression training phase is the temperature-sensitive load sequence.

[0041] Furthermore, the acquired load dataset is defined as follows: ,in Indicates the number of samples in the dataset. The total load consumption and environmental information for each area of ​​the building, or input variables, This corresponds to the temperature-sensitive load data, i.e., the label variables. (Dataset) Based on the type of label, they can be divided into two main categories, one of which is... This indicates that the temperature-sensitive load data is not empty, meaning that each total load data sample has a corresponding temperature-sensitive load data label; another type is... This indicates that the temperature-sensitive load data is empty, meaning the sample has a missing label value. In actual buildings, the second type of data samples is usually much more numerous than the first type. The input variable can be defined as... ,in This represents the time dimension of the input variables. Let be the feature dimension at each timestamp.

[0042] Furthermore, area type labels are used to describe the spatial or functional similarity between different areas, and can be determined based on floor plan layout, room number, room function, area, orientation, building envelope conditions, equipment configuration, or clustering results. In this embodiment, rooms with the same number or function on different floors of a multi-story building are assigned the same or similar area type labels.

[0043] In this embodiment, area type labels are generated based on building floor plans, room numbers, room functions, room areas, orientations, building envelope conditions, and equipment configurations. For example, in a multi-story building, areas 1 on the 4th floor, 1 on the 5th floor, and 1 on the 6th floor can have the same area type label; areas 1 on the 4th floor and 2 on the 4th floor can have different area type labels. If the building floor plans are not completely identical, clustering can be performed based on the similarity of area, orientation, function, and historical total load curves, and the clustering results can be used as area type labels. This approach makes the method not limited to buildings with completely identical floor structures.

[0044] Step 2: Decomposition of temperature-sensitive load based on semi-supervised contrastive regression learning. Construct a semi-supervised contrastive regression learning model. Using regional total load data and environmental data as input, extract the time series representation of total load through self-supervised contrastive learning. Utilize temperature-sensitive load labeled data of several floor areas and combine it with area type labels for semi-supervised regression training. By leveraging the spatial structural similarity between areas with the same area type label on different floors, the temperature-sensitive load is decomposed from the total load data of floor areas with unmeasured temperature-sensitive load.

[0045] Specifically, such as Figure 2As shown, this invention constructs a semi-supervised contrastive regression framework (SCRF). It includes five core components: a data augmentation module, an encoder, a self-supervised decoder, a regression decoder, and a discriminator. The data augmentation module generates different augmented views of the input sequence. The encoder maps the augmented total regional load sequence and environmental features into a high-dimensional temporal representation. The self-supervised decoder reconstructs the original total regional load sequence based on the temporal representation. The regression decoder outputs the temperature-sensitive load decomposition result based on the temporal representation. The discriminator adaptively selects the sequence segments that need to be augmented in the next round of training based on the error between the augmented and reconstructed sequences.

[0046] In this embodiment, as Figure 3 As shown, the data amplification module employs a segmented amplification strategy: Let the input sequence be The length is The length of each sequence segment is Then the entire input sequence can be divided into There are sequence segments, among which This represents the floor function. Therefore, ,in , Indicates length is The A sequence segment. Further, let... This indicates the number of sequence segments that need to be amplified, i.e., from the total number of sequence segments. Select Amplify each sequence segment. Let This indicates the selected segment of the original input sequence. and They represent respectively to The sequence segments obtained after segmented jitter amplification and segmented masked amplification. The two amplification methods are defined as follows:

[0047] in, Indicates that it follows the mean. variance is Gaussian noise, This represents the Gaussian noise scaling factor. Segmented amplification can perturb local peak segments, variation segments, or segments with large reconstruction errors while preserving the overall temporal structure of the load, thereby improving the self-supervised representation learning effect.

[0048]

[0049] For mask augmentation, the selected sequence segment can also be replaced with a preset mask value.

[0050] In this embodiment, the input sequence length is set to 96, and the segment length is set to 24, so each input sequence is divided into 4 segments. Two segments are selected from the 4 segments for amplification each time. Segment jitter is achieved by adding Gaussian noise related to the standard deviation of the selected segments, and segment masking is achieved by setting the selected segment data to zero. Segment amplification is only used in the self-supervised pre-training stage. In the semi-supervised regression training stage, the original input sequence can be directly fed into the encoder.

[0051] Furthermore, self-supervised pre-training is performed using a self-supervised decoder: Specifically, the self-supervised pre-training phase utilizes only regional total load data and environmental data, without requiring temperature-sensitive load labels. Two augmented views are generated for the same input sequence, which, after passing through a self-supervised encoder, yield corresponding representation sequences. The self-supervised decoder then reconstructs the original regional total load sequence based on these representation sequences. In the self-supervised process, the self-supervised loss function is set as follows: The details are as follows:

[0052]

[0053]

[0054]

[0055] In the above formula, and They represent the first The time step The original and reconstructed values ​​of each feature. This indicates the batch size during model training. and These represent the characterization sequences obtained after the two amplified views are encoded, where... and Indicates the first The sample at the th The representation vector corresponding to each time step. This is an indicator function that takes the value 1 when the condition inside the parentheses is true, and 0 otherwise. This represents the mean square reconstruction error. Will As positive sample pairs, they are compared with the representations of other time steps in the same sample; Then, the representations of identical positive samples are compared with those of other samples in the same batch. Through the set self-supervised loss, the encoder can learn the temporal variation pattern of the regional total load sequence and the inter-sample difference characteristics.

[0056] Furthermore, segment selection is adaptively amplified via a discriminator: Specifically, in the SCRF framework, the discriminator is mainly used to calculate the loss value and rationally select the sequence segments to be amplified. Let... and These represent the encoder's response based on the input sequence during the current training iteration. The reconstructed sequences corresponding to the two generated amplified views. The discriminator first calculates the absolute difference between each amplified sequence and its reconstructed sequence. :

[0057] Subsequently, a kernel of size 1 is applied to each difference sequence. Max pooling operation:

[0058] The pooled sequence is divided into... A length of The sequence segment. Let express The middle belongs to the first The subvectors of each sequence segment. For each sequence segment, the maximum value is taken as the error of that sequence segment:

[0059] For each augmented view, select the one with the largest error. These sequence segments constitute the amplified sequence segment set for the next training iteration. :

[0060] This adaptive selection mechanism allows the encoder to focus more on sequence segments with poor reconstruction results, thereby accelerating model convergence and improving representation quality. Data augmentation is only used during the self-supervised training phase; during supervised training, the input sequences are not augmented but are directly input into the encoder.

[0061] Furthermore, supervised regression training: In this embodiment, the supervised regression training phase is carried out on the basis of the self-supervised pre-trained model. The regression decoder is trained by freezing the parameters of the self-supervised encoder, or the encoder and regression decoder can be fine-tuned together in the later stage of training.

[0062] To utilize spatial similarity across floors or areas, such as Figure 4As shown, this invention proposes Multi-label Aware Loss (MLA Loss). For samples in the same training batch, a positive sample set and a negative sample set are constructed based on the region type label. Samples with the same region type label or spatial similarity meeting a preset threshold constitute positive sample pairs; samples with different region type labels or similarity below a preset threshold constitute negative sample pairs. MLA Loss calculation method:

[0063]

[0064] In the above formula, Represents cosine similarity. This represents a nonlinear transformation used to map amplified sequences into high-dimensional representation features. and This represents the representation obtained by the encoder. and These represent the positive sample set and the negative sample set defined by the region type label, respectively. This is used to maximize the similarity between samples of the same region type while minimizing the similarity between samples of different region types. and These represent the actual temperature-sensitive load and the decomposed temperature-sensitive load, respectively. Through MLA Loss, the model can transfer the decomposed knowledge of temperature-sensitive loads from a small number of measured areas to structurally similar but unmeasured areas, thereby improving decomposition accuracy under conditions of scarce temperature-sensitive load labels.

[0065] It should be noted that, as Figure 5 As shown, SCRF is a semi-supervised regression framework whose training and application process includes three stages: self-supervised training, regression training, and practical application. In the self-supervised training stage, only the dataset needs to be used. Total load data and environmental data No need to use the corresponding temperature-sensitive load data The loss function used in this stage is During the regression training phase, only data from a single floor with temperature-sensitive load labels were used. Based on the total load representation reconstructed from the encoder, the regression decoder is trained to effectively learn the mapping relationship between temperature-sensitive load and total load. The loss function used in this stage is... After model training is complete, the total load data with unknown temperature-sensitive loads can be input into the model. After reconstruction by the encoder and decoding by the regression decoder, the corresponding temperature-sensitive loads can be obtained. This enables the decomposition of temperature-sensitive loads.

[0066] The parameters of the preferred embodiments are shown in the table below: Table 1. SCRF Structure and Hyperparameter Settings

[0067]

[0068] Step 3: Data-driven thermal comfort response modeling with physical mechanism constraints. Construct and train a data-driven thermal comfort response model with physical mechanism constraints. This model includes a physical thermal model branch and a data-driven residual branch. This is to describe the dynamic relationship between temperature-sensitive loads and indoor thermal comfort state, such as... Figure 7 As shown, this invention constructs a data-driven thermal comfort response model constrained by physical mechanisms. The model includes a physical thermal model branch and a data-driven residual branch.

[0069] The physical thermal model branch is used to describe building thermal inertia and basic heat exchange processes. For example... Figure 6 As shown, the 3R2C physical model is used as the space heat exchange model. The governing equations of the 3R2C model can be expressed as:

[0070]

[0071] in, This indicates the indoor air temperature, i.e., the physical reference indoor temperature. Indicates the wall temperature. Indicates outdoor air temperature; , and These represent the thermal resistance between indoor air and the wall, between indoor air and outdoor air, and between the wall and outdoor air, respectively. and These represent the heat capacity of indoor air and walls, respectively. The formula for calculating the heat power acting on the building's thermal process after conversion from temperature-sensitive load is as follows: ,in, This represents the performance coefficient of temperature-sensitive load equipment. Used to indicate the direction of heating or cooling; it is set to 1 for heating and -1 for cooling. Represents discrete time points within the control cycle. Indicates the next adjustment time point within the adjustment cycle. This indicates the time interval between adjacent control points.

[0072] Subsequently, the thermal resistance and heat capacity parameters in the RC model can be calibrated using genetic algorithms, particle swarm optimization, Bayesian optimization, or other parameter identification methods to minimize the error of the physical model in predicting indoor temperature.

[0073] This invention employs a residual structure to couple a data-driven model with a 3R2C physical model. Preferably, a BiGRU network is used as the data-driven model, but GRU, LSTM, TCN, or Transformer time-series networks can also be used. The signal transmission process is as follows: In At any given time, the outdoor temperature and temperature-sensitive load As the input boundary conditions of the 3R2C model, the output of the 3R2C model predicts the indoor temperature. BIGRU will use historical temperature-sensitive loads. and historical environmental data Used as input for model training, through Historical residual data is constructed and used as target values ​​for model training to train the BIGRU model; during the prediction phase, the BiGRU uses temperature-sensitive loads. Environmental information, and the residuals from the previous BIGRU model output. and the hidden state of the previous moment As input, the output is the predicted residual. The final indoor temperature is expressed as... The proposed residual coupling structure enables the physical thermal model to provide a reference trajectory that conforms to thermodynamic laws, allowing the data-driven model to be nonlinearly corrected on the physical reference, thereby reducing the risk of overfitting or physically inconsistent predictions by the pure data-driven model under unfamiliar operating conditions.

[0074] The 3R2C physical model is used as the physical baseline branch. First, the thermal resistance and heat capacity parameters of the 3R2C model are calibrated using data with measured indoor temperature values. The calibration objective is to minimize the RMSE between the indoor temperature predicted by the physical model and the measured indoor temperature. In a preferred embodiment, a genetic algorithm is used for parameter optimization, with a population size of 200, a maximum number of iterations of 300, a crossover probability of 0.8, and a mutation probability of 0.05.

[0075] After completing the physical model calibration, the thermal resistance and heat capacity parameters are fixed, and the physical reference indoor temperature is output using the 3R2C model. Then, a BiGRU residual model is constructed, using the temperature-sensitive load, outdoor temperature, outdoor humidity, time characteristics, and historical residuals obtained from SCRF decomposition as inputs to predict the residuals. The final indoor temperature prediction result is:

[0076] In a preferred embodiment, the BiGRU network adopts a 2-layer structure with a hidden layer size of 32, a dropout rate of 0.5, an RMSE loss function, an Adam optimizer, 20,000 training epochs, and a learning rate of 0.01.

[0077] Step 4: Energy flexibility potential assessment based on thermal comfort constraints. The power sequence of temperature-sensitive loads in each region is used as the benchmark temperature-sensitive load sequence. An allowable range for indoor thermal comfort is set, and a data-driven thermal comfort response model is used to obtain the predicted sequence of indoor thermal comfort status within the control period. Under the condition that the predicted sequence of indoor thermal comfort status meets the allowable range for indoor thermal comfort, the optimized temperature-sensitive load power sequence is obtained with the goal of minimizing the energy consumption of temperature-sensitive loads within the control period. Then, the energy flexibility potential rate is calculated by summing the energy consumption of the benchmark temperature-sensitive load and the optimized temperature-sensitive load.

[0078] During the cooling season, the indoor temperature setting can be increased. This corresponds to the adjusted upper limit of the temperature; during the heating season, the indoor temperature setting can be lowered. This corresponds to the adjusted lower temperature limit. For consistency, the thermal comfort constraint can be written as:

[0079] in, and These are the adjusted lower and upper limits for indoor thermal comfort, respectively.

[0080] The optimization objective can be expressed as:

[0081] in, To optimize the power of candidate temperature-sensitive loads during the process, The time interval between adjacent control points. This represents the total number of time points within the control period.

[0082] The energy flexibility potential is characterized by the energy flexibility potential rate; The baseline temperature-sensitive load energy consumption and the optimized temperature-sensitive load energy consumption for each region are calculated as follows:

[0083] No. The energy flexibility potential rate for each region is calculated as follows:

[0084] No. The energy flexibility potential rate of each floor is calculated as follows:

[0085] The energy flexibility potential of the entire building is calculated as follows:

[0086] in, The first decomposition obtained in step 2 The region in the first Reference temperature-sensitive load power at each time point For the first The region in the first Optimized power of temperature-sensitive load at each time point The time interval between adjacent time points. This represents the total number of time points within the control period. For the first The set of areas contained in each floor The set of all areas encompassed by the target building. , and These are the energy flexibility potential rates at the regional, floor, and whole building levels, respectively.

[0087] In this embodiment, the CU-BEMS dataset is used as an example. The 3rd floor is selected as the labeled floor, and the 4th to 7th floors are selected as unlabeled floors. Areas with similar structures in each floor are selected as the basis for area type labeling. The total load of the unlabeled floor area is decomposed into temperature-sensitive load using SCRF, and then the 3R2C-BiGRU residual thermal comfort response model is used to predict indoor temperature changes.

[0088] Taking the adjustment of the cooling setpoint by +1.0℃ as an example, as shown in Table 2, the total demand of the temperature-sensitive load of the entire building in the CU-BEMS dataset experimental building can be reduced from 2953.77 kW·h to 2274.32 kW·h, corresponding to an energy flexibility potential of 23.00%. This provides a huge energy-saving margin during peak load periods. It also shows that this invention can assess the flexibility potential of the remaining floors of a building by acquiring only the temperature-sensitive load data of a single floor, thereby assessing the overall flexibility potential of the building. The corresponding results can provide a basis for building managers to formulate zoned energy-saving control strategies.

[0089] Table 2. Demand and energy-saving potential of temperature-sensitive loads in different areas of the experimental building before and after optimization (F3Z1 represents area 1 on the 3rd floor).

[0090] It should be noted that, without departing from the technical concept of this invention, the encoder and regression decoder in SCRF are not limited to Transformer, and can also employ LSTM, GRU, TCN, attention networks, or other time-series models. The self-supervised contrastive loss is not limited to TS2Vec type loss, and can also employ other time-series contrastive losses that can constrain temporal consistency and instance discriminability.

[0091] The physical thermal model is not limited to the 3R2C model; 2R2C, 4R3C, state-space gray box thermal models, or other physical models that can describe the thermal inertia of a building can also be used. The data-driven residual model is not limited to BiGRU; GRU, LSTM, TCN, Transformer, or hybrid neural networks can also be used.

[0092] The optimization algorithm for temperature-sensitive loads is not limited to genetic algorithms; it can also employ particle swarm optimization, Bayesian optimization, dynamic programming, model predictive control, or other optimization algorithms. The optimization objective is not limited to minimizing the energy consumption of temperature-sensitive loads; it can be extended to minimizing operating costs, reducing peak loads, improving demand response benefits, or balancing energy consumption and comfort deviations into a multi-objective optimization approach.

[0093] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for assessing the building energy flexibility potential based on semi-supervised load decomposition, characterized in that, Includes the following steps: Step 1: Obtain the total load data, environmental data, indoor thermal comfort status data, area type labels, and temperature-sensitive load label data for several floors and areas of the target building, and perform data preprocessing; the area type labels are used to characterize the similarity of different areas in terms of function, spatial location, floor layout, room number, area, orientation, building envelope conditions, and equipment configuration; the indoor thermal comfort status data includes indoor temperature. Step 2: Construct a semi-supervised contrastive regression learning model. Using regional total load data and environmental data as input, extract the time series representation of total load through self-supervised contrastive learning. Utilize temperature-sensitive load label data of several floor areas and combine it with area type labels for semi-supervised regression training. By utilizing the spatial structural similarity between areas with the same area type label on different floors, the temperature-sensitive load is decomposed from the total load data of floor areas with unmeasured temperature-sensitive load. Step 3: Construct and train a data-driven thermal comfort response model constrained by physical mechanisms. The data-driven thermal comfort response model constrained by physical mechanisms includes a physical thermal model branch and a data-driven residual branch. Step 4: Use the temperature-sensitive load power sequence of each region as the benchmark temperature-sensitive load sequence, set the indoor thermal comfort allowable range, and use the data-driven thermal comfort response model to obtain the indoor thermal comfort state prediction sequence within the control period. Under the condition that the indoor thermal comfort state prediction sequence meets the indoor thermal comfort allowable range, with the goal of minimizing the temperature-sensitive load energy consumption within the control period, obtain the optimized temperature-sensitive load power sequence; then, sum the benchmark temperature-sensitive load energy consumption and the optimized temperature-sensitive load energy consumption respectively to calculate the energy flexibility potential rate.

2. The method according to claim 1, characterized in that, In step 2, the semi-supervised contrastive regression learning model includes a data augmentation module, an encoder, a self-supervised decoder, a regression decoder, and a discriminator. The data augmentation module is used to generate different augmented views of the input sequence, the encoder is used to extract time series representations, the self-supervised decoder is used to reconstruct the total regional load sequence, the regression decoder is used to output the temperature-sensitive load decomposition results, and the discriminator is used to adaptively select the sequence segments to be augmented in the next round of training based on the reconstruction error.

3. The method according to claim 2, characterized in that, The data amplification module employs a segmented amplification strategy: the input sequence is divided into several segments according to a preset segment length, and one or more segments are selected for local amplification; the local amplification includes segmented dithering amplification and segmented masking amplification. The segmented jitter amplification is defined as follows: in, Indicates that it follows the mean. variance is Gaussian noise, This is the Gaussian noise scaling factor. Represents the input sequence, where , Indicates length is The A sequence segment, and They represent respectively to The sequence segments obtained after segmented jitter amplification and segmented mask amplification; The segmented mask augmentation is defined as follows: 。 4. The method according to claim 2, characterized in that, The self-supervised contrastive learning employs a self-supervised loss function. , represented as: in, and They represent the first The time step Original and reconstructed values ​​of each feature. This indicates the batch size during model training. This represents the number of time steps in the input sequence. This represents the number of features at each time step. , and These represent the sample, time step, and feature index, respectively. and These represent the characterization sequences obtained after the two amplified views are encoded, where... and Indicates the first The sample at the th The representation vector corresponding to each time step This is an indicator function that takes the value 1 when the condition within the parentheses is true, and 0 otherwise. This represents the mean square reconstruction error. Will As positive sample pairs, they are compared with the representations of other time steps in the same sample; Then the characteristics of the same positive sample pairs are compared with those of other samples in the same batch.

5. The method according to claim 2, characterized in that, The adaptive amplification segment selection of the discriminator includes: calculating the absolute difference between the amplified sequence and the reconstructed sequence output by the self-supervised decoder. For each absolute difference The sequence execution kernel size is Max pooling operation; calculate the error of each sequence segment according to the preset segmentation method; select the segment with the largest error. Each sequence segment is used as a candidate segment for amplification in the next training iteration.

6. The method according to claim 4, characterized in that, In step 2, the semi-supervised regression training uses a multi-label perceptual contrastive loss function, expressed as follows: in, Indicates calculation and Cosine similarity; This represents a nonlinear transformation used to map the temporal representation of the encoder output to a contrastive feature space; and This represents the representation obtained by the encoder. and These represent the positive sample set and the negative sample set, respectively, as defined by the region type label; This is used to maximize the similarity between samples of the same region type while minimizing the similarity between samples of different region types. and These represent the actual temperature-sensitive load and the temperature-sensitive load obtained from decomposition, respectively.

7. The method according to claim 6, characterized in that, In step 2, the training process of the semi-supervised contrastive regression learning model includes: the loss function used in the self-supervised pre-training stage is... Temporal representation learning is performed using total regional load data and environmental data from all areas of all floors of the building. The loss function used in the semi-supervised regression training phase is... The model utilizes temperature-sensitive load labeled data from a floor area and trains on a regression decoder based on the total load time series representation extracted by the encoder to effectively learn the mapping relationship between temperature-sensitive load and total load. In the practical application stage, the total load data and environmental data from areas where temperature-sensitive load is not measured are input into the trained model, and the corresponding temperature-sensitive load decomposition results are output.

8. The method according to claim 1, characterized in that, The training method for the data-driven thermal comfort response model constrained by the physical mechanism mentioned in step 3 is as follows: By utilizing historical temperature-sensitive load power sequences, historical environmental data, and corresponding measured indoor thermal comfort state sequences, a data-driven thermal comfort response model constrained by physical mechanisms is trained. A physical reference response reflecting the building's thermal inertia is generated using the physical thermal model, and the residual between the measured indoor thermal comfort state and the physical reference response is used as the training target for nonlinear correction of the data-driven model. This results in a data-driven thermal comfort response model constrained by physical mechanisms that can predict the indoor thermal comfort state sequence within the control period based on candidate temperature-sensitive load power sequences, corresponding environmental data, and the indoor thermal comfort state at the start of the control period.

9. The method according to claim 8, characterized in that, The method for obtaining the indoor thermal comfort state prediction sequence is as follows: the physical thermal model branch is a 3R2C physical model, which can output the physical reference indoor temperature sequence within the control period. The data-driven residual branch will incorporate historical temperature-sensitive loads. and historical environmental data The training input used for the data-driven residual branch is obtained through... Construct historical residual sequence data, where For historical real indoor temperature series data, The target value is used as the training value for the data-driven residual branch, and the data-driven residual branch is trained accordingly. During the forecasting phase, the candidate temperature-sensitive load power sequence within the control period will be... and corresponding environmental data Input the trained data to drive the residual branch, according to Output residual prediction sequence ,in This represents the residual prediction mapping function composed of recurrent neural networks, long short-term memory networks, gated recurrent unit networks, bidirectional gated recurrent unit networks, temporal convolutional networks, or Transformer temporal networks. Indicates the network parameters obtained through training; and according to Obtain the indoor thermal comfort state prediction sequence .

10. The method according to claim 8, characterized in that, The physical thermal model is a 3R2C physical model, and its governing equations are: in, This indicates the indoor air temperature, i.e., the physical reference indoor temperature. Indicates the wall temperature. Indicates outdoor air temperature; , and These represent the thermal resistance between indoor air and the wall, between indoor air and outdoor air, and between the wall and outdoor air, respectively. and These represent the heat capacity of indoor air and walls, respectively. The formula for calculating the heat power acting on the building's thermal process after conversion from temperature-sensitive load is as follows: ,in, This represents the performance coefficient of temperature-sensitive load equipment. Used to indicate the direction of heating or cooling; it is set to 1 for heating and -1 for cooling. Represents discrete time points within the control cycle. Indicates the next adjustment time point within the adjustment cycle. This indicates the time interval between adjacent control points.

11. The method according to claim 1, characterized in that, The allowable range of indoor thermal comfort mentioned in step 4 is determined as follows: During the cooling season, the upper limit of the baseline indoor temperature is increased by the amount of adjustment of the preset indoor temperature setting; during the heating season, the lower limit of the baseline indoor temperature is decreased by the amount of adjustment of the preset indoor temperature setting. The predicted values ​​of indoor thermal comfort at each time point within the control period satisfy: ,in , These are the adjusted lower and upper limits for indoor thermal comfort, respectively.

12. The method according to claim 1, characterized in that, In step 4, the candidate temperature-sensitive load power sequences of each region within the control period are used as optimization variables. One or more of the following methods are employed: genetic algorithm, particle swarm optimization, Bayesian optimization, dynamic programming, or model predictive control. Under the condition that the indoor temperature prediction sequence corresponding to the candidate temperature-sensitive load power sequence meets the allowable range for indoor thermal comfort, the energy consumption of the temperature-sensitive load is solved. Minimum optimized temperature-sensitive load power sequence The optimization objective is expressed as: in, To optimize the power of candidate temperature-sensitive loads during the process, The time interval between adjacent control points. This represents the total number of time points within the control cycle.

13. The method according to claim 1, characterized in that, In step 4, the energy flexibility potential is characterized by the energy flexibility potential rate; The baseline temperature-sensitive load energy consumption and the optimized temperature-sensitive load energy consumption for each region are calculated as follows: No. The energy flexibility potential rate for each region is calculated as follows: No. The energy flexibility potential rate of each floor is calculated as follows: The energy flexibility potential of the entire building is calculated as follows: in, The first decomposition obtained in step 2 The region in the first Reference temperature-sensitive load power at each time point For the first The region in the first Optimized power of temperature-sensitive load at each time point The time interval between adjacent time points. This represents the total number of time points within the control period. For the first The set of areas contained in each floor The set of all areas encompassed by the target building. , and These are the energy flexibility potential rates at the regional, floor, and whole building levels, respectively.

14. The method according to claim 1, characterized in that, The environmental data includes one or more of the following: outdoor temperature, outdoor humidity, solar radiation, time characteristics, weekday characteristics, weekday identifiers, and holiday identifiers; the temperature-sensitive load includes one or more of the following: heating, ventilation, air conditioning, or heat pump system loads that vary with external meteorological conditions or indoor temperature setpoints.

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