Multi-identification intelligent sensing method for safety risk of tunnel and underground engineering

Abstract

The invention belongs to the field of engineering technology risk management, and provides a tunnel and underground engineering safety risk multi-identification intelligent sensing method. The implementation of the method comprises the following steps: firstly, acquiring multi-modal data on a tunnel and an underground engineering structure by using a multi-identification method; constructing and training an engineering safety risk prediction model; and performing dynamic quantitative evaluation on the tunnel and underground engineering safety risk by using the trained engineering safety risk prediction model. According to the method, the multi-recognition perception technology and the artificial intelligence technology are combined, safety risk information in the tunnel and underground engineering can be observed, the method can be applied to safety risk management in the tunnel and underground engineering, the safety risk level of the tunnel in the construction period and the operation period is evaluated, and the safety risk management efficiency is improved. And the safe state of the tunnel and the underground engineering can be expressed quickly and accurately.

Description

Technical Field

[0001] The invention belongs to the field of engineering technology risk management. Background Art

[0002] Tunnels and underground projects have played an important role in improving infrastructure connectivity. In the construction and operation of tunnels and underground projects, the sources of risks are complex and diverse, and the consequences are serious. How to properly manage the safety risks of tunnels and underground projects is an important issue that needs to be addressed. Risk management theory and actual projects show that the safety risks of tunnels and underground projects can be controlled. It is essentially a problem from uncertainty to certainty, and in this process, the perception of engineering safety risks is crucial. Therefore, the digital transformation brought about by the rapid development of various sensors and artificial intelligence will change the way engineering services are provided. Through timely intervention to prevent and avoid engineering safety risk accidents, develop an engineering safety risk assessment system obtained from multi-sensory perception data to help build and manage multi-stakeholder communities. Multimodal data is used to predict risks such as engineering diseases and accidents. By identifying high-risk sources and taking proactive intervention measures to ensure construction and operation safety, resilience recovery, improved health and extended life, this is the highest pursuit of engineering.

[0003] At present, observation methods are often used as risk management techniques for the identification of engineering safety risks, which can effectively deal with uncertainties in engineering design and construction. However, traditional observation methods rely on single monitoring variables and empirical methods to judge risks, lack comprehensive and systematic data support, and are prone to misjudgment of risk identification, and cannot provide effective guarantees for on-site safety. On this basis, evaluating the safety status of tunnels and underground projects by image acquisition is a more reliable method, but traditional image-based safety risk analysis can only identify structural status within the visible light range and cannot perform full-band visual acquisition. In addition, for the analysis of safety risks, traditional single variable (such as deformation, cracks, water seepage, etc.) evaluation methods and multivariate evaluation methods relying on linear combinations are difficult to reveal the implicit coupling relationship between variables, resulting in inaccurate safety risk analysis. Summary of the invention

[0004] In view of the above problems, the present invention proposes a Multi-Insight Smart Sensing (MISS) method for safety risks of tunnels and underground projects.

[0005] This method is based on the concept of insight method. It collects tactile, visual, acoustic, gas and other multi-sensory perception data of tunnels and underground projects in all directions, and uses these data as an important information source for safety risk prediction of tunnels and underground projects. Artificial intelligence is used to process these data scientifically, quickly and accurately to obtain safety status. It aims to break through the current situation of single information source for safety risk assessment of tunnels and underground projects, low processing efficiency and accuracy, and realize full-time and comprehensive safety risk perception during the construction and operation of tunnels and underground projects.

[0006] Technical solution of the present invention:

[0007] The multi-aware intelligent perception method for safety risks of tunnels and underground projects collects multi-modal data of tunnels and underground projects in all directions, and processes the acquired multi-modal data with artificial intelligence technology to achieve safety risk prediction of tunnels and underground projects. The implementation of this method includes the following steps:

[0008] Step 1: In tunnels and underground projects, use multi-sensing devices to collect multi-modal data to gain insights into the safety risks of tunnels and underground projects;

[0009] Step 2: Use artificial intelligence technology and engineering mechanics models to build and train engineering safety risk prediction models;

[0010] Step 3: When new multimodal engineering data appears, use the trained engineering safety risk prediction model to conduct dynamic quantitative assessment of tunnel and underground engineering safety risks.

[0011] Advantages and beneficial effects of the present invention:

[0012] The present invention is a multi-aware intelligent perception method for tunnel and underground engineering safety risks based on the insight method. The method combines multi-awareness perception technology with artificial intelligence technology, and can gain insight into safety risk information in tunnels and underground engineering. It can be applied to safety risk management in tunnels and underground engineering, evaluate the safety risk level of tunnels during construction and operation periods, and achieve rapid and accurate representation of the safety status of tunnels and underground engineering.

[0013] The present invention proposes for the first time that multi-sensing technology should be used in tunnels and underground projects to obtain data of different modes by collecting sensor fulcrums of different physical quantities (touch, sight, sound, and gas). Compared with the previous observation method and traditional single physical quantity analysis, it can more comprehensively perceive the safety status of underground structures.

[0014] The present invention proposes for the first time to use artificial intelligence to predict safety risks using multimodal data (numbers, images, gases, sounds) obtained in tunnels and underground projects. Traditional safety assessment methods are difficult to quantitatively process multimodal information and can only rely on empirical judgment. Therefore, the method proposed in the present invention is more reasonable and effective. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 Schematic diagram of the overall process of the present invention.

[0016] Figure 2 Example GPT-tunnel and underground engineering safety risk prediction model training process. DETAILED DESCRIPTION

[0017] Terminology explanation:

[0018] Insight method: Insight method refers to the process of moving from "appearance" to "inner" of the system to be studied. In tunnels and underground projects, traditional observation methods can only obtain surface phenomena through sensors and monitoring equipment of a single physical quantity, while the insight method can conduct in-depth analysis of the collected data to discover the internal laws of the overall system of tunnels and underground projects, reveal the essence of the problem, and thus more comprehensively predict potential risks, thereby guiding design and construction adjustments.

[0019] Multi-sensory perception: the ability to acquire and process information through multiple sensory methods. This perception is not limited to a single sense organ or signal source, but through multi-modal perception means, such as vision, hearing, touch, smell, etc., to fully understand and analyze the information in the environment. It emphasizes the coordination and complementarity between multiple perception means to achieve a deeper understanding of complex environments.

[0020] Multimodal data: data in multiple forms obtained from sensors, devices or systems of different types or sources. These data may include visual, auditory, textual, tactile, taste, olfactory information, such as images, videos, audio, speech, text, etc. The characteristic of multimodal data is that they come from multiple dimensions or perceptual channels, so they can provide multiple levels of understanding of the same thing from different perspectives.

[0021] The present invention uses multi-perception technology based on the insight method to identify and judge safety risks in tunnels and underground projects. Specifically, it uses multi-modal data acquired through collection fulcrums (simulated touch, sound, gas, and taste) and on-site machines (simulated vision) to obtain monitoring data, and uses artificial intelligence technology to process the acquired multi-modal data to predict safety risks in tunnels and underground projects.

[0022] The technical solution provided by the present application will be further described below in conjunction with specific embodiments and accompanying drawings. The advantages and features of the present application will become more apparent with the following description.

[0023] Example

[0024] The multi-aware intelligent perception method for tunnel and underground engineering safety risks proposed in the present invention collects multimodal data of tunnels and underground engineering in all directions, processes the acquired multimodal data in combination with artificial intelligence technology, and realizes safety risk prediction of tunnels and underground engineering.

[0025] The overall technical route of the present invention is as follows Figure 1 shown.

[0026] Step 1. In tunnels and underground projects, collect multimodal data through multi-sensing devices to gain insight into the safety risks of tunnels and underground projects.

[0027] The multi-knowledge intelligent perception of the present invention includes the following aspects:

[0028] 1.1 Tactile Perception

[0029] Through the bidirectional tilt sensing fulcrum, convergence tilt sensing fulcrum, water leakage sensing fulcrum and flexible deformation sensing series fulcrum of tunnels and underground projects, the deformation and leakage of tunnels and underground projects are measured from all angles. The data collected is numerical, and the data is transmitted through wireless monitoring technology. Take tunnel projects as an example:

[0030] The bidirectional inclination sensing supports are symmetrically arranged on the arch waists on both sides of the tunnel, with a measuring range of -30° to +30° and an accuracy of 0.01°.

[0031] The convergence inclination angle sensing fulcrum is arranged on the arch waist on one side of the tunnel, with a measuring range of -90° to +90° and an accuracy of 0.002°.

[0032] The water leakage sensing points are arranged at the joints of the tunnel segments, and data is collected through distributed fiber optic sensing technology with a collection frequency of 10 Hz, a spatial resolution of 1 mm, and a sensing accuracy of ±1 με.

[0033] The flexible deformation sensing series fulcrums are arranged longitudinally on the multi-ring segments, with a measuring range of 0 to 25.4 mm and an accuracy of 0.003 mm.

[0034] 1.2 Visual Perception

[0035] Different from traditional image acquisition methods, the present invention uses the electromagnetic wave spectrum to capture the image of the object to be measured, perceives the characteristics of the object to be measured based on the image features, and performs visual acquisition of tunnels and underground projects through digital cameras, hyperspectral cameras, and laser scanning. Visible light wave grayscale value / speckle cloud is used to perceive the apparent disease detection of tunnels and underground projects and the characteristics of rock tunnels, and dynamic safety risk analysis is performed. Two-dimensional and three-dimensional risk characterization is identified from four types of structural features: structural surface, weak interlayer, groundwater, and joints and fissures, to achieve dynamic safety risk analysis. The data type collected is pixel-type image, and data is transmitted through wireless monitoring technology.

[0036] Digital camera: collects surface crack characteristics of tunnels and underground engineering structures in the visible spectrum (400-1000nm).

[0037] Hyperspectral camera: collects intensity characteristics of tunnels and underground engineering structures in the near-infrared spectrum (900-1700nm).

[0038] Laser scanning: Use laser (600-700nm) to scan and collect point cloud information of tunnels and underground engineering structures.

[0039] 1.3 Acoustic Perception

[0040] The knock detection unit automatically knocks on the concrete, and uses artificial intelligence to determine whether there is any concrete surface peeling, thereby determining the potential threat to tunnels and underground projects. The data collected is audio type, and data is transmitted through wireless monitoring technology.

[0041] Tapping frequency: 10-20Hz.

[0042] Impact force: 1-2 Newtons.

[0043] Sensor sensitivity: Accelerometer sensitivity 0.1m / s 2 , the microphone sensitivity is 0.1dB.

[0044] Sampling frequency: 10kHz.

[0045] 1.4 Gas Perception

[0046] By monitoring the concentration of carbon monoxide and methane (CO+CH4) gas, combined with monitoring alarms, early warning can be used to prevent suffocation and explosion accidents. The data collected is the concentration value, and the data is transmitted through wireless monitoring technology.

[0047] Concentration detection range: 0-100% LEL (Lower Explosive Limit).

[0048] Minimum detection resolution: 0.01%LEL.

[0049] Step 2. Use artificial intelligence technology and engineering mechanics models to build and train engineering safety risk prediction models

[0050] A project safety risk prediction model is constructed, which evaluates the safety risk level of tunnels and underground projects by performing data fusion analysis on the input multimodal data (including text descriptions, numerical features, audio data, and image data).

[0051] The engineering safety risk prediction model includes: four sub-models, namely, a text feature extraction model, a numerical feature processing model, an audio feature extraction model, and an image feature extraction model; and a classifier. The four sub-models extract text, numerical, audio, and image features respectively, and fuse these extracted features through a feature fusion layer. The classifier analyzes and processes the fused features and outputs a risk category.

[0052] (1) Multimodal data representation and input

[0053] A multimodal dataset is formed based on the multimodal data obtained in step 1.

[0054] Let X = {x1, x2, ..., x n} represents a multimodal dataset consisting of n samples. Each sample x i It contains the following parts (the characteristics here refer to the mathematical expression of multimodal data):

[0055] Text features: represents the text description vector of the i-th sample, d T dimensional text vector.

[0056] Numerical features: Represents the numerical data of the i-th sample, d N is the dimension of the numerical feature.

[0057] Audio Features: Represents the audio feature of the i-th sample, which is extracted by Fourier Transform to obtain d A dimensional frequency domain vector.

[0058] Image features: Represents the image features of the i-th sample. After the convolutional neural network (CNN) extracts the pixel information of the entire image, d I -dimensional image vector.

[0059] Therefore, the overall representation of the i-th sample is:

[0060] x i =[T i ,N i ,A i ,I i ]

[0061] in,

[0062] (2) Multimodal feature extraction and fusion

[0063] The following four sub-models are used to extract text, numerical, audio and image features respectively:

[0064] Text feature extraction modelf T : Through the Transformer deep learning model, the contextual information of the text is extracted and a high-dimensional vector representation is generated to map the text description into a high-dimensional vector: where k T It is the dimension of mapping text description into high-dimensional vector. Examples of specific hyperparameter values ​​are:

[0065] Hyperparameters Value illustrate Word embedding dimension (d_model) 768 Representing the dimension of word vector Number of heads (h) 12 Number of heads for multi-head attention Number of encoder layers (N) 12 The number of encoder or decoder stacking layers Feedforward neural network dimension (d_ff) 3072 Usually 4 times the word embedding dimension Learning Rate 5e-5 (pre-training) Control parameter update step size Batch Size 32 The number of samples used in each training Training Steps 100,000 Usually trained on a large corpus Dropout Rate 0.1 Preventing Overfitting Weight Decay 0.01 Controlling model complexity Warm-up Steps 4000 The number of steps to initially increase the learning rate Max Sequence Length 512 Maximum supported input sequence length

[0066] Numerical feature processing model f N : Use the Z-score normalization function to ensure that each feature has the same scale, normalize the numerical data and map it into high-dimensional features: where k N It is the dimension along which numerical data is normalized and mapped into high-dimensional features.

[0067] Audio feature extraction model f A :The time domain signal is converted into frequency domain representation through Fourier Transform to identify the spectral characteristics of the signal. The Mel-frequency cepstral coefficient (MFCC) is used to process the audio signal on a Mel frequency scale, and the extracted features are used for speech recognition and audio analysis: where k A It is the dimension of the audio vector after Mel frequency scaling.

[0068] Image feature extraction model f I :Extract local features and spatial information through a ResNet-based convolutional neural network (CNN) model: where k I It is the vector dimension for extracting local features and spatial information. Examples of specific hyperparameter values ​​are:

[0069]

[0070] These extracted features are fused through the feature fusion layer:

[0071]

[0072] Among them, z i is the sample x i The final fusion feature.

[0073] The dimension of the fused feature vector is the sum of the dimensions of the text description, numerical features, audio data, and image data.

[0074] (3) Classifier

[0075] Classifier fC The fusion feature z i Import and export risk categories

[0076]

[0077] in, Indicates the predicted safety risk level of tunnels and underground projects, where 1 represents very low risk, 2 represents low risk, 3 represents medium risk, 4 represents high risk, and 5 represents very high risk.

[0078] (4) Loss Function and Optimization

[0079] Let the risk level label be The goal of the engineering safety risk prediction model is to minimize the cross entropy loss function L:

[0080]

[0081] Among them, θ represents the model parameters, is the prediction sample x i The probability of belonging to class c.

[0082] (5) Engineering safety risk prediction model training

[0083] The parameter θ is updated by the gradient descent optimization algorithm:

[0084]

[0085] Where η is the learning rate, is the gradient of the loss function with respect to the parameters θ.

[0086] Step 3. When new multimodal engineering data appears, use the trained engineering safety risk prediction model to dynamically and quantitatively evaluate the safety risks of tunnels and underground projects.

[0087] After training is completed, for new multimodal data input x i , the risk category predicted by the engineering safety risk prediction model output

[0088]

[0089] By comparing with the true category y i Compare the results and calculate the accuracy of the model:

[0090]

[0091] in, is the Kronecker delta function, used to represent the predicted category and the true category y i Are they equal?

[0092] In response to various safety risks in the construction and operation of tunnels and underground projects, the implementation example uses holographic intelligence theory to simulate human sensory methods, and uses vision, hearing, smell, taste and touch to holographically perceive the safety risks in tunnels and underground projects. The acquired monitoring data is transmitted to the intelligent gateway in the form of a wireless network, uploaded to the cloud platform server cluster, and stored in the holographic concept space. A GPT-tunnel safety risk prediction model is developed based on the GPT4 Explore module. The multi-modal data obtained by multi-perception intelligently analyzes the safety risk value of tunnels and underground projects, and conducts diversified third-party data transfer. The specific process is as follows ( Figure 2 ):

[0093] Among them, upload Excel file: click the "Upload Data" button to upload the table file with the suffix .xlsx to the project. The file should contain the image ID and the corresponding text description. Upload compressed file: upload the .zip file containing rock image information to the project. The image file name should be its ID, and these IDs should correspond to the ID fields in the .xlsx file.

[0094] After uploading the data, configure the parameters for model training. The specific parameter configuration is as follows:

[0095] 1.Receive the file with the suffix"xlsx"uploaded by the user

[0096] 2.These two files are numerical data and feature data extracted from images

[0097] 3.Their image classifications all correspond to the types "1,2,3,4,5"

[0098] 4.If the field attributes in the "xlsx" file are missing, fill the minthrough the model algorithm.

[0099] 5.Perform feature engineering such as data standardization on thedata

[0100] 6.After making a judgment,you need to compare the accuracy with thefinal answer sent to you by the user,and then feedback the accuracy to theuser

[0101] 7.Communication with users should be formal

[0102] 8.The purpose of this model is to accurately predict the strength ofrocks (predicted classification"1.2.3.4.5").

[0103] 9.You need to use your model to process predicted classificationnumerical data and images.

[0104] 10.Answer questions in Chinese

[0105] 11.When you need to increase the computing power of the algorithm youdon't need to ask the user if they want to increase the computing power.Youjust need to perform the calculation directly,and finally just need tofeedback the prediction results to the user

[0106] 12.id and ID are the same field name

[0107] The above embodiment proposes a Multi-Insight Smart Sensing (MISS) method that integrates multi-insight sensing technology and artificial intelligence technology and is suitable for the safety risks of tunnels and underground projects, and realizes the comprehensive assessment and representation of the safety status of tunnels and underground projects. It has the following innovative features:

[0108] 1. Based on the concept of insight method, multi-modal data in the construction and operation of tunnels and underground projects is obtained through multi-awareness perception technology. The data source is more comprehensive, ensuring the authenticity, extensiveness and effectiveness of the data source for safety risk assessment in tunnels and underground projects.

[0109] 2. The acquired multimodal data is processed through artificial intelligence technology, and the safety risk prediction of tunnels and underground projects is carried out based on large models. Compared with traditional safety risk prediction methods, it has the advantages of processing multimodal data, interactivity and high precision.

[0110] 3. The present invention comprehensively considers tunnel inclination, convergence deformation, longitudinal uneven deformation, water leakage, working face characteristics, tunnel lining surface, and the concentration of carbon monoxide and methane. Through the perception of tunnel engineering holographic data, the present invention comprehensively evaluates tunnel safety risks, and the assessment accuracy, reliability and safety are higher.

[0111] 4. The present invention aims at the safety risks of the long-term evolution of tunnel structural performance throughout the entire life cycle, including the tunnel construction period and the operation period. The holographic data source has a wider dimension, so it can ensure the safety of tunnel construction and operation from a longer time span.

[0112] The above description is only a description of the preferred embodiments of the present application, and is not intended to limit the scope of the present application. Any changes or modifications made by any person skilled in the art based on the above disclosed technical contents shall be deemed as equivalent effective embodiments and shall fall within the scope of protection of the technical solution of the present application.

Claims

1. A multi-aware intelligent perception method for safety risks in tunnels and underground projects, characterized in that: By collecting multimodal data of tunnels and underground projects in all directions and processing the acquired multimodal data with artificial intelligence technology, safety risk prediction of tunnels and underground projects can be achieved; The implementation of this method includes the following steps: Step 1: In tunnels and underground projects, use multi-sensing devices to collect multi-modal data to gain insights into the safety risks of tunnels and underground projects; Step 2: Use artificial intelligence technology and engineering mechanics models to build and train engineering safety risk prediction models; Step 3: When new multimodal engineering data appears, use the trained engineering safety risk prediction model to conduct dynamic quantitative assessment of tunnel and underground engineering safety risks.

2. The tunnel and underground engineering safety risk multi-awareness intelligent perception method according to claim 1, characterized in that: Multi-aware intelligent perception includes the following four aspects: tactile perception, visual perception, acoustic perception, and gas perception. Correspondingly, the data collection device facilities in step 1 are: Tactile perception: Through the bidirectional inclination sensing fulcrum, convergence inclination sensing fulcrum, water leakage sensing fulcrum and flexible deformation sensing series fulcrums for tunnels and linear underground projects, the deformation and leakage of tunnels and underground projects are measured in all directions and at multiple angles; the data type collected is numerical; Visual perception: Use the electromagnetic spectrum to capture the image of the object being measured, perceive the characteristics of the object being measured based on the image features, and use digital cameras, hyperspectral cameras, and laser scanning to perform visual acquisition of tunnels and underground projects; the data type collected is pixel-type images; Acoustic perception: Use the knock detection unit to automatically knock on the concrete, and use artificial intelligence to determine whether there is any concrete surface peeling, thereby determining the potential threats to tunnels and underground projects; the data type collected is audio type; Gas perception: By monitoring the concentration of carbon monoxide and methane, combined with monitoring alarms, early warnings can be issued to prevent suffocation and explosion accidents; the data type collected is concentration values.

3. The tunnel and underground engineering safety risk multi-awareness intelligent perception method according to claim 1, characterized in that: The second step: Construct an engineering safety risk prediction model, which evaluates the safety risk level of tunnels and underground projects by performing data fusion analysis on the input multi-modal data; The multimodal data includes text description, numerical features, audio data and image data; The engineering safety risk prediction model includes: four sub-models, namely, a text feature extraction model, a numerical feature processing model, an audio feature extraction model, and an image feature extraction model; and a classifier; the four sub-models extract text, numerical, audio and image features respectively, fuse these extracted features through a feature fusion layer, and the classifier outputs a risk category by analyzing and processing the fused features.

4. The tunnel and underground engineering safety risk multi-awareness intelligent perception method according to claim 3 is characterized in that: The second step: Among them, multimodal data representation and input: Forming a multimodal data set based on the multimodal data obtained in step one; Let X = {x1, x2, …, x n } represents a multimodal dataset consisting of n samples, each sample x i Contains the following parts: Text features: represents the text description vector of the i-th sample, d T -dimensional text vector; Numerical features: Represents the numerical data of the i-th sample, d N is the dimension of the numerical feature; Audio Features: Represents the audio feature of the i-th sample, which is extracted by Fourier Transform to obtain d A dimensional frequency domain vector; Image features: Represents the image features of the i-th sample. After the convolutional neural network (CNN) extracts the pixel information of the entire image, d I dimensional image vector; Therefore, the overall representation of the i-th sample is: x i =[T i ,N i ,A i ,I i ] in, Among them, multimodal feature extraction and fusion: The following four sub-models are used to extract text, numerical, audio and image features respectively: Text feature extraction modelf T : Through the Transformer deep learning model, the contextual information of the text is extracted and a high-dimensional vector representation is generated to map the text description into a high-dimensional vector: where k T It is the dimension of mapping text description into high-dimensional vector; Numerical feature processing model f N : Use the Z-score normalization function to ensure that each feature has the same scale, normalize the numerical data and map it into high-dimensional features: where k N It is the dimension in which numerical data is normalized and mapped into high-dimensional features; Audio feature extraction model f A :The time domain signal is converted into frequency domain representation through Fourier Transform to identify the spectral characteristics of the signal; the audio signal is processed by Mel frequency cepstral coefficient (MFCC) to perform Mel frequency scaling, and the extracted features are used for speech recognition and audio analysis: where k A is the dimension of the audio vector after Mel frequency scaling; Image feature extraction model f I :Extract local features and spatial information through a ResNet-based convolutional neural network (CNN) model: where k I It is the vector dimension for extracting local features and spatial information; These extracted features are fused through the feature fusion layer: Among them, z i is the sample x i The final fusion characteristics of The dimension of the fused feature vector is the sum of the dimensions of the text description, numerical features, audio data, and image data; Among them, the classifier: Classifier f C The fusion feature z i Import and export risk categories in, Indicates the predicted safety risk level of tunnels and underground projects, where 1 represents extremely low risk, 2 represents low risk, 3 represents medium risk, 4 represents high risk, and 5 represents extremely high risk.

5. The tunnel and underground engineering safety risk multi-awareness intelligent perception method according to claim 4, characterized in that: The second step is to train the engineering safety risk prediction model: Loss function and optimization: The goal of the engineering safety risk prediction model is to minimize the cross entropy loss function L: Among them, θ represents the model parameters, is the prediction sample x i The probability of belonging to category c; The parameter θ is updated by the gradient descent optimization algorithm: Where η is the learning rate, is the gradient of the loss function with respect to the parameter θ.

Images