Fire temperature field analysis and prediction method based on artificial intelligence

Abstract

The invention discloses a fire temperature field analysis and prediction method based on artificial intelligence, and the method comprises the steps: 1, deploying a distributed heterogeneous sensor network, and outputting a heterogeneous original data set; 2, constructing a space-time diagram convolutional recursive network based on the heterogeneous original data set in the step 1; 3, constructing a heat conduction constraint generative adversarial network by using the spatial-temporal characteristic matrix and the dynamic graph structure in the step 2; 4, constructing a multi-modal fusion prediction model; 5, carrying out self-feedback closed-loop dynamic calibration; the method has the beneficial effects that a fire temperature field prediction system with physical interpretability and environmental adaptability is constructed through a heterogeneous data collaborative closed loop, a physical constraint conduction closed loop and a model self-evolution closed loop, and accurate and reliable technical support is provided for early fire early warning and emergency decision making.

Description

Technical Field

[0001] The present invention relates to the field of fire temperature field prediction and analysis, and in particular to a fire temperature field analysis and prediction method based on artificial intelligence. Background Art

[0002] Fire accidents are sudden and destructive. Rapid and accurate prediction of fire temperature field changes is crucial for personnel evacuation, fire rescue decision-making, and reducing disaster losses. Traditional fire monitoring mainly relies on a single type of sensor, which has problems such as large monitoring blind spots and single data dimensions. It is difficult to fully capture the dynamics of fires in complex scenarios. At the same time, existing prediction models mostly use fixed network structures and cannot adapt to the dynamic changes of fire heat flow, resulting in a lack of accuracy in prediction results. With the development of technologies such as the Internet of Things and artificial intelligence, how to use multi-source heterogeneous data and intelligent algorithms to build a high-precision, adaptive fire temperature field prediction system has become a research hotspot and technical difficulty in the current fire protection field. Summary of the Invention

[0003] The purpose of the present invention is to solve the above-mentioned problems, and therefore proposes a fire temperature field analysis and prediction method based on artificial intelligence.

[0004] The purpose of the present invention can be achieved through the following technical solutions: A fire temperature field analysis and prediction method based on artificial intelligence, comprising: Step 1: Deploy a distributed heterogeneous sensor network and output heterogeneous raw data sets; Step 2: Build a spatiotemporal graph convolutional recursive network based on the heterogeneous original dataset in step 1; Step 3: Using the spatiotemporal feature matrix and dynamic graph structure from step 2, construct a heat conduction constrained generative adversarial network. Step 4: Construction of multimodal fusion prediction model; Step 5: Self-feedback closed-loop dynamic calibration.

[0005] Furthermore, the step 1 is specifically as follows: Construct an air-ground collaborative sensor network in the monitoring area, including: Ground level: Distributed fiber optic temperature sensors are laid along building corridors and forest trails, with a temperature measurement node set up every 10 meters. Smoke / CO sensors are also deployed simultaneously to obtain environmental parameters, including temperature. ,humidity , carbon monoxide concentration , based on environmental parameters to form ground sensor time series data ; Air base: deploy 3 drones in formation, equipped with infrared thermal imagers, cruise in a triangular coverage mode, and generate temperature field thermal imaging images at a predetermined frequency. .

[0006] Furthermore, the UAV is equipped with an RTK positioning system, which uses coordinate mapping to , the physical location of the ground sensor node is matched one by one with the pixel points of the UAV thermal image, where, Represents spatial position coordinates.

[0007] Furthermore, the step 2 specifically includes: Spatial feature extraction: Convert ground node coordinates (x, y, z) into graph network nodes and construct a spatial adjacency matrix using the K-nearest neighbor algorithm , thermal imaging of drones Perform superpixel segmentation to extract the temperature mean and gradient variance of each block as spatial context features ; Temporal feature modeling: Time series data from ground sensors Extracting time-dependent features using LSTM networks ,in Represents a series of time-varying data sequences collected by ground sensors. Indicates the Ground sensors in Temperature data collected at all times, Indicates that from t-30 seconds to The first time in this period The temperature data sequence of the sensor is input into the LSTM network, and the final output is That is, the time-dependent features are extracted, and the spatiotemporal gating unit is designed, through the weight matrix Fusion and , output node-level spatiotemporal features ; Construct the spatiotemporal feature matrix: , This matrix is ​​a real number matrix with N rows and 128 columns. Each row of the matrix corresponds to a node, i.e., a ground node or a UAV superpixel block. Each column represents a feature dimension, which includes temperature change trend, fluctuation amplitude, and spatial neighborhood relationship. Build a dynamic graph structure: obtain the three-dimensional coordinates of the drone in real time, and divide the monitoring area into spatial grid units, each of which corresponds to a node in the graph structure; The infrared thermal imager carried by the drone collects real-time temperature data from each grid cell and calculates the heat conduction weight between nodes. If two grid cells are spatially adjacent and meet the heat conduction conditions, an edge connection is established in the graph structure. The heat conduction conditions include being within a distance threshold and having a heat conduction medium. Map the relationship between nodes and edges into an N×N dimensional spatial adjacency matrix .

[0008] Furthermore, the step three specifically includes: Will As the initial input of the generator, it contains the spatiotemporal characteristic information of the fire scene; It is used to constrain the spatial topological relationship in the generation process and is passed to the generator and discriminator as conditional input. The partial differential equation constraint module is embedded in the generator, and the heat conduction equation is converted into a form that can be processed by the neural network through the differentiable solver, so that the generated data conforms to the real heat conduction law. At the same time, combined with the spatiotemporal characteristics Generate simulation data of fire temperature field; Construct a dual discriminator structure, one discriminator is used to distinguish real fire data from generated data, and the other discriminator is based on The rationality of the spatial structure of the generated data is judged, and a dual discrimination mechanism is used to enhance the robustness of the model. The gradient penalty technique is used to stabilize the training process, and the residual term of the heat conduction equation is introduced into the loss function to ensure that the generated data meets both the adversarial learning objectives and the physical constraints of heat conduction. Enhanced training dataset, .

[0009] The step 4 specifically includes: Enhanced training dataset based on step 3 and the spatiotemporal feature matrix of step 2 , train multimodal prediction models; Output node-level temperature series , with prediction confidence ,in, The output of the model is The temperature prediction value of each node from 1 second to 600 seconds in the future represents the temperature prediction result of a single node; The first The confidence formula reflects the credibility of the prediction result by calculating the difference between the predicted value and the current true value. The smaller the difference, the higher the confidence. The closer to 1; Mark areas exceeding critical temperatures based on spatiotemporal feature matrix, node-level temperature series, and prediction confidence .

[0010] The step five specifically includes: According to the prediction confidence of step 4 and critical regions , start the UAV self-feedback calibration mechanism, calibration trigger condition, when <0.7 or Area ≥50m Boundary flight, using LiDAR to obtain 3D coordinates, combined with infrared thermal imagers to generate sub-meter temperature field true values , is a spatial point; 2 When the drone enters the fine scanning mode, the drone will For nodes with confidence lower than the threshold, use Perform weighted fusion with the sensor data in step 1 to generate calibrated data ; The model predicts the temperature value The actual temperature value Weighted summation by prediction confidence to generate calibrated data , when the prediction confidence When the value exceeds the set range, the calibrated data moves closer to the predicted value; when the prediction confidence is not within the set range, the calibrated data moves closer to the actual temperature value, thereby achieving optimal calibration of the confidence prediction result. The calibrated data is fed back into the spatiotemporal graph convolutional recurrent network in step 2 to update the spatiotemporal graph features. , triggering the gradient update of the model in step 4.

[0011] Compared with the prior art, the present invention has the following beneficial effects: High coverage and precise monitoring: Through the coordinated deployment of heterogeneous air-ground sensors and precise coordinate mapping, the problem of single-sensor monitoring blind spots is effectively resolved. This improves monitoring coverage in complex environments and enables more comprehensive acquisition of fire scene data. The self-feedback drone calibration mechanism, combined with multi-timescale fine-tuning, enables autonomous model optimization, eliminating reliance on manually annotated data updates. This improves model adaptation speed and enables rapid adaptation to new scenarios. Through the collaborative closed loop of heterogeneous data, the physical constraint transmission closed loop and the model self-evolution closed loop, a fire temperature field prediction system with physical interpretability and environmental adaptability was constructed, providing accurate and reliable technical support for early fire warning and emergency decision-making. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] To facilitate understanding by those skilled in the art, the present invention is further described below with reference to the accompanying drawings.

[0013] Figure 1 This is a flow chart of a fire temperature field analysis and prediction method based on artificial intelligence of the present invention. DETAILED DESCRIPTION

[0014] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0015] See also Figure 1 As shown, a fire temperature field analysis and prediction method based on artificial intelligence includes: Step 1: Deploy a distributed heterogeneous sensor network and output heterogeneous raw data sets; Step 2: Build a spatiotemporal graph convolutional recursive network based on the heterogeneous original dataset in step 1; Step 3: Using the spatiotemporal feature matrix and dynamic graph structure from step 2, construct a heat conduction constrained generative adversarial network. Step 4: Construction of multimodal fusion prediction model; Step 5: Self-feedback closed-loop dynamic calibration.

[0016] The step 1 is specifically as follows: Construct an air-ground collaborative sensor network in the monitoring area, including: Ground level: Distributed fiber optic temperature sensors are laid along building corridors and forest trails, with a temperature measurement node set up every 10 meters. Smoke / CO sensors are also deployed simultaneously to obtain environmental parameters, including temperature. ,humidity , carbon monoxide concentration , based on environmental parameters to form ground sensor time series data ; Air base: deploy 3 drones in formation, equipped with infrared thermal imagers, cruise in a triangular coverage mode, and generate temperature field thermal imaging images at a predetermined frequency. .

[0017] The UAV is equipped with an RTK positioning system, through coordinate mapping , the physical location of the ground sensor node is matched one by one with the pixel points of the UAV thermal image, where, Represents spatial position coordinates.

[0018] During use, distributed fiber optic temperature sensors and smoke / CO sensors were deployed every 10 meters along the corridor on the ground floor, successfully capturing the early abnormal temperature rise caused by aging electrical lines, which was 3°C higher than the ambient temperature. At the same time, a formation of three drones cruised in a "triangle coverage" mode, and discovered hidden heat sources near the roof vents through infrared thermal imagers. Through air-ground collaboration, traditional single-point monitoring was upgraded to area perception + three-dimensional monitoring, which increased the coverage of temperature data collection and provided multi-source data support with high temporal and spatial resolution for fire warning.

[0019] The second step specifically includes: Spatial feature extraction: Convert ground node coordinates (x, y, z) into graph network nodes and construct a spatial adjacency matrix using the K-nearest neighbor algorithm , thermal imaging of drones Perform superpixel segmentation to extract the temperature mean and gradient variance of each block as spatial context features ; Temporal feature modeling: Time series data from ground sensors Extracting time-dependent features using LSTM networks ,in Represents a series of time-varying data sequences collected by ground sensors. Indicates the Ground sensors in Temperature data collected at all times, Indicates that from t-30 seconds to The first time in this period The temperature data sequence of the sensor is input into the LSTM network, and the final output is That is, the time-dependent features are extracted, and the spatiotemporal gating unit is designed, through the weight matrix Fusion and , output node-level spatiotemporal features ; Construct the spatiotemporal feature matrix: , This matrix is ​​a real number matrix with N rows and 128 columns. Each row of the matrix corresponds to a node, i.e., a ground node or a UAV superpixel block. Each column represents a feature dimension, which includes temperature change trend, fluctuation amplitude, and spatial neighborhood relationship. Build a dynamic graph structure: obtain the three-dimensional coordinates of the drone in real time, and divide the monitoring area into spatial grid units, each of which corresponds to a node in the graph structure; The infrared thermal imager carried by the drone collects real-time temperature data from each grid cell and calculates the heat conduction weight between nodes. If two grid cells are spatially adjacent and meet the heat conduction conditions, an edge connection is established in the graph structure. The heat conduction conditions include being within a distance threshold and having a heat conduction medium. Map the relationship between nodes and edges into an N×N dimensional spatial adjacency matrix .

[0020] The spatiotemporal feature matrix expands the fire scene information dimension from single temperature data to 128 dimensions. The dynamic graph structure can update the heat conduction path in real time. The model's ability to express the characteristics of complex scenes is improved, providing richer input information for subsequent predictions.

[0021] The step three specifically includes: Will As the initial input of the generator, it contains the spatiotemporal characteristic information of the fire scene; It is used to constrain the spatial topological relationship in the generation process and is passed to the generator and discriminator as conditional input. The partial differential equation constraint module is embedded in the generator, and the heat conduction equation is converted into a form that can be processed by the neural network through the differentiable solver, so that the generated data conforms to the real heat conduction law. At the same time, combined with the spatiotemporal characteristics Generate simulation data of fire temperature field; Construct a dual discriminator structure, one discriminator is used to distinguish real fire data from generated data, and the other discriminator is based on The rationality of the spatial structure of the generated data is judged, and a dual discrimination mechanism is used to enhance the robustness of the model. The gradient penalty technique is used to stabilize the training process, and the residual term of the heat conduction equation is introduced into the loss function to ensure that the generated data meets both the adversarial learning objectives and the physical constraints of heat conduction. Enhanced training dataset, .

[0022] The data augmentation strategy expands the size of the training dataset and improves the generalization ability of the model in low-data scenarios. At the same time, the physical constraints of the generated data ensure the reliability of the model predictions.

[0023] The step 4 specifically includes: Enhanced training dataset based on step 3 and the spatiotemporal feature matrix of step 2 , train multimodal prediction models; Output node-level temperature series , with prediction confidence ,in, The output of the model The temperature prediction value of each node from 1 second to 600 seconds in the future represents the temperature prediction result of a single node; The first The confidence formula reflects the credibility of the prediction result by calculating the difference between the predicted value and the current true value. The smaller the difference, the higher the confidence. The closer to 1; Mark areas exceeding critical temperatures based on spatiotemporal feature matrix, node-level temperature series, and prediction confidence .

[0024] Multimodal fusion improves the model's prediction accuracy for fire development, reduces node-level temperature prediction errors, and regional-level thermal maps provide intuitive visual support for emergency decision-making.

[0025] The step five specifically includes: According to the prediction confidence of step 4 and critical regions , start the UAV self-feedback calibration mechanism, calibration trigger condition, when <0.7 or Area ≥50m Boundary flight, using LiDAR to obtain 3D coordinates, combined with infrared thermal imagers to generate sub-meter temperature field true values , is a spatial point; 2 When the drone enters the fine scanning mode, the drone will For nodes with confidence lower than the threshold, use Perform weighted fusion with the sensor data in step 1 to generate calibrated data ; The model predicts the temperature value The actual temperature value Weighted summation by prediction confidence to generate calibrated data , when the prediction confidence When the value exceeds the set range, the calibrated data moves closer to the predicted value; when the prediction confidence is not within the set range, the calibrated data moves closer to the actual temperature value, thereby achieving optimal calibration of the confidence prediction result. The calibrated data is fed back into the spatiotemporal graph convolutional recurrent network in step 2 to update the spatiotemporal graph features. , triggering the gradient update of the model in step 4.

[0026] The self-feedback closed-loop mechanism realizes the adaptive optimization of the model, reduces the prediction error, and at the same time improves the prediction efficiency of the model in similar scenarios through data accumulation, significantly enhancing the long-term reliability of the system.

[0027] Example 1: Taking a large commercial complex as an application scenario, a distributed heterogeneous sensor network was deployed with sensors laid every 10 meters in the corridors of the commercial complex, with a total of 300 temperature measurement nodes deployed. 50 smoke / CO sensors were installed in key areas such as the underground parking lot and equipment room. At the same time, three drones equipped with infrared thermal imagers were deployed, cruising at an altitude of 15 meters and in "triangle coverage" mode to collect a thermal image every 20 seconds. After two hours of normal monitoring, the following ground time series data were generated: Contains 7200 sets of temperature, humidity, and CO concentration data with 350 nodes and a 1Hz sampling rate, including drone thermal imaging: The sequence consists of 360 100×100 pixel images, with spatiotemporal thermal image annotation data: The precise coordinate mapping between 300 ground nodes and thermal imaging pixels was established using the drone RTK system; The spatiotemporal feature fusion and graph structure modeling are carried out. 300 ground nodes and thermal imaging superpixels are divided into 500 blocks by the algorithm, and a spatiotemporal graph containing 800 nodes is constructed. The K-nearest neighbor algorithm is used to calculate the Euclidean distance between nodes to generate a spatial adjacency matrix. The LSTM network is used to extract the 30-second time window features of the ground sensor data, and finally a spatiotemporal graph is formed. Feature matrix; Step 3: Physical constraint generation adversarial data enhancement. For the only 100 sets of real fire simulation data for this scenario, the heat conduction constraint generation adversarial network TC-GAN was used to generate 600 sets of virtual data. The generator input included the initial temperature of 35°C at the fire point (B2 floor distribution room). By embedding the Fourier heat conduction equation (material thermal diffusion coefficient α = 0.01m 2 / s), generating a 60-minute temperature evolution sequence. The results show that the error in the thermal diffusion rate of the generated data is 7.2%, and the positioning deviation of the fire point is 1.8m, effectively expanding the training set to 700 groups. Step 4: Constructing a multimodal fusion prediction model. Ground sensor data, drone thermal imaging features, and spatiotemporal feature matrices are input into the model. In a simulated fire test, the model outputs the following 5 minutes after the fire: Node-level prediction: The predicted temperature of the B2-floor distribution room node rises from 50°C to 82°C (the actual value is 85°C), with a confidence level of 0.85. Regional-level thermal map: The high-temperature diffusion path is accurately marked, and the affected area is predicted to reach 120m in 10 minutes. 2 (Actual 115m 2 ); Step 5: Self-feedback closed-loop dynamic calibration When the model's prediction confidence for a certain area of ​​the underground parking lot drops to 0.65, the drone is triggered to perform a detailed scan, and the true value is obtained through the lidar and infrared thermal imager. The calibration temperature is obtained through weighted fusion. The calibration data was fed back to update the ST-GCRN model. After three calibration iterations, the prediction confidence for this region increased to 0.88, and the model prediction error decreased by 42%. The calibration data was incorporated into TC-GAN training monthly to continuously optimize the model's generalization capabilities.

[0028] The preferred embodiments of the present invention disclosed above are intended only to help illustrate the present invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the present invention to the specific embodiments described. Obviously, many modifications and variations are possible based on the content of this specification. These embodiments are selected and described in detail in this specification to better explain the principles and practical applications of the present invention, thereby enabling those skilled in the art to better understand and utilize the present invention. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A fire temperature field analysis and prediction method based on artificial intelligence, characterized in that: include: Step 1: Deploy a distributed heterogeneous sensor network and output heterogeneous raw data sets; Step 2: Build a spatiotemporal graph convolutional recursive network based on the heterogeneous original dataset in step 1; Step 3: Using the spatiotemporal feature matrix and dynamic graph structure from step 2, construct a heat conduction constrained generative adversarial network. Step 4: Construction of multimodal fusion prediction model; Step 5: Self-feedback closed-loop dynamic calibration.

2. The fire temperature field analysis and prediction method based on artificial intelligence according to claim 1 is characterized in that: The step 1 is specifically as follows: Construct an air-ground collaborative sensor network in the monitoring area, including: Ground level: Distributed fiber optic temperature sensors are laid along building corridors and forest trails, with a temperature measurement node set up every 10 meters. Smoke / CO sensors are also deployed simultaneously to obtain environmental parameters, including temperature. ,humidity , carbon monoxide concentration , based on environmental parameters to form ground sensor time series data ; Air base: deploy 3 drones in formation, equipped with infrared thermal imagers, cruise in a triangular coverage mode, and generate temperature field thermal imaging images at a predetermined frequency. .

3. The fire temperature field analysis and prediction method based on artificial intelligence according to claim 2 is characterized in that: The UAV is equipped with an RTK positioning system, through coordinate mapping , the physical location of the ground sensor node is matched one by one with the pixel points of the UAV thermal image, where, Represents spatial position coordinates.

4. The fire temperature field analysis and prediction method based on artificial intelligence according to claim 3 is characterized in that: The second step specifically includes: Spatial feature extraction: Convert ground node coordinates (x, y, z) into graph network nodes and construct a spatial adjacency matrix using the K-nearest neighbor algorithm , thermal imaging of drones Perform superpixel segmentation to extract the temperature mean and gradient variance of each block as spatial context features ; Temporal feature modeling: Time series data from ground sensors Extracting time-dependent features using LSTM networks ,in Represents a series of time-varying data sequences collected by ground sensors. Indicates the Ground sensors in Temperature data collected at all times, Indicates from t-30 seconds to The first time in this period The temperature data sequence of the sensor is input into the LSTM network, and the final output is That is, the time-dependent features are extracted, and the spatiotemporal gating unit is designed, through the weight matrix Fusion and , output node-level spatiotemporal features ; Construct the spatiotemporal feature matrix: , This matrix is ​​a real number matrix with N rows and 128 columns. Each row of the matrix corresponds to a node, i.e., a ground node or a UAV superpixel block. Each column represents a feature dimension, which includes temperature change trend, fluctuation amplitude, and spatial neighborhood relationship. Build a dynamic graph structure: obtain the three-dimensional coordinates of the drone in real time, and divide the monitoring area into spatial grid units, each of which corresponds to a node in the graph structure; The infrared thermal imager carried by the drone collects real-time temperature data from each grid cell and calculates the heat conduction weight between nodes. If two grid cells are spatially adjacent and meet the heat conduction conditions, an edge connection is established in the graph structure. The heat conduction conditions include being within a distance threshold and having a heat conduction medium. Map the relationship between nodes and edges into an N×N dimensional spatial adjacency matrix .

5. The fire temperature field analysis and prediction method based on artificial intelligence according to claim 4 is characterized in that: The step three specifically includes: Will As the initial input of the generator, it contains the spatiotemporal characteristic information of the fire scene; It is used to constrain the spatial topological relationship in the generation process and is passed to the generator and discriminator as conditional input. The partial differential equation constraint module is embedded in the generator, and the heat conduction equation is converted into a form that can be processed by the neural network through the differentiable solver, so that the generated data conforms to the real heat conduction law. At the same time, combined with the spatiotemporal characteristics Generate simulation data of fire temperature field; Construct a dual discriminator structure, one discriminator is used to distinguish real fire data from generated data, and the other discriminator is based on The rationality of the spatial structure of the generated data is judged, and a dual discrimination mechanism is used to enhance the robustness of the model. The gradient penalty technique is used to stabilize the training process, and the residual term of the heat conduction equation is introduced into the loss function to ensure that the generated data meets both the adversarial learning objectives and the physical constraints of heat conduction. Enhanced training dataset, .

6. The fire temperature field analysis and prediction method based on artificial intelligence according to claim 5 is characterized in that: The step 4 specifically includes: Enhanced training dataset based on step 3 and the spatiotemporal feature matrix of step 2 , train multimodal prediction models; Output node-level temperature series , with prediction confidence ,in, The output of the model is The temperature prediction value of each node from 1 second to 600 seconds in the future represents the temperature prediction result of a single node; The first The confidence formula reflects the credibility of the prediction result by calculating the difference between the predicted value and the current true value. The smaller the difference, the higher the confidence. The closer to 1; Mark areas exceeding critical temperatures based on spatiotemporal feature matrix, node-level temperature series, and prediction confidence .

7. The fire temperature field analysis and prediction method based on artificial intelligence according to claim 6 is characterized in that: The step five specifically includes: According to the prediction confidence of step 4 and critical regions , start the UAV self-feedback calibration mechanism, calibration trigger condition, when <0.7 or Area ≥50m Boundary flight, using LiDAR to obtain 3D coordinates, combined with infrared thermal imagers to generate sub-meter temperature field true values , is a spatial point; 2 When the drone enters the fine scanning mode, the drone will For nodes with confidence lower than the threshold, use Perform weighted fusion with the sensor data in step 1 to generate calibrated data ; The model predicts the temperature value The actual temperature value Weighted summation by prediction confidence to generate calibrated data , when the prediction confidence When the value exceeds the set range, the calibrated data moves closer to the predicted value; when the prediction confidence is not within the set range, the calibrated data moves closer to the actual temperature value, thereby achieving optimal calibration of the confidence prediction result. The calibrated data is fed back into the spatiotemporal graph convolutional recurrent network in step 2 to update the spatiotemporal graph features. , triggering the gradient update of the model in step 4.

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