LSTM and GRU

 

Long Short-Term Memory (LSTM) Networks

LSTMs are a type of Recurrent Neural Network (RNN) designed to handle sequential data with long-term dependencies.

Key Features:

Cell State: Preserves information over long periods.

Gates: Control information flow (input, output, and forget gates).

Hidden State: Temporary memory for short-term information.

Related Technologies:

Recurrent Neural Networks (RNNs): Basic architecture for sequential data.

Gated Recurrent Units (GRUs): Simplified version of LSTMs.

Bidirectional RNNs/LSTMs: Process input sequences in both directions.

Encoder-Decoder Architecture: Used for sequence-to-sequence tasks.

Real-World Applications:

Language Translation

Speech Recognition

Text Generation

Time Series Forecasting

GRUs are an alternative to LSTMs, designed to be faster and more efficient while still capturing long-term dependencies.

Key Differences from LSTMs:

Simplified Architecture: Fewer gates (update and reset) and fewer state vectors.

Faster Computation: Reduced number of parameters.

Technical Details for LSTMs and GRUs:

LSTM Mathematical Formulation:

Let x_t be the input at time t, h_t be the hidden state, and c_t be the cell state.

Input Gate: i_t = sigmoid(W_i * x_t + U_i * h_(t-1) + b_i)

Forget Gate: f_t = sigmoid(W_f * x_t + U_f * h_(t-1) + b_f)

Cell State Update: c_t = f_t * c_(t-1) + i_t * tanh(W_c * x_t + U_c * h_(t-1) + b_c)

Output Gate: o_t = sigmoid(W_o * x_t + U_o * h_(t-1) + b_o)

Hidden State Update: h_t = o_t * tanh(c_t)

Parameters:

W_i, W_f, W_c, W_o: Weight matrices for input, forget, cell, and output gates.

U_i, U_f, U_c, U_o: Weight matrices for hidden state.

b_i, b_f, b_c, b_o: Bias vectors.

GRU Mathematical Formulation:

Let x_t be the input at time t, h_t be the hidden state.

Update Gate: z_t = sigmoid(W_z * x_t + U_z * h_(t-1) + b_z)

Reset Gate: r_t = sigmoid(W_r * x_t + U_r * h_(t-1) + b_r)

Hidden State Update: h_t = (1 - z_t) * h_(t-1) + z_t * tanh(W_h * x_t + U_h * (r_t * h_(t-1)) + b_h)

Parameters:

W_z, W_r, W_h: Weight matrices for update, reset, and hidden state.

U_z, U_r, U_h: Weight matrices for hidden state.

b_z, b_r, b_h: Bias vectors.

Here's a small mathematical example for an LSTM network:

Example:

Suppose we have an LSTM network with:

Input dimension: 1

Hidden dimension: 2

Output dimension: 1

Input at time t (x_t)

x_t = 0.5

Previous Hidden State (h_(t-1)) and Cell State (c_(t-1))

h_(t-1) = [0.2, 0.3]

c_(t-1) = [0.4, 0.5]

Weight Matrices and Bias Vectors

W_i = [[0.1, 0.2], [0.3, 0.4]]

W_f = [[0.5, 0.6], [0.7, 0.8]]

W_c = [[0.9, 1.0], [1.1, 1.2]]

W_o = [[1.3, 1.4], [1.5, 1.6]]

U_i = [[1.7, 1.8], [1.9, 2.0]]

U_f = [[2.1, 2.2], [2.3, 2.4]]

U_c = [[2.5, 2.6], [2.7, 2.8]]

U_o = [[2.9, 3.0], [3.1, 3.2]]

b_i = [0.1, 0.2]

b_f = [0.3, 0.4]

b_c = [0.5, 0.6]

b_o = [0.7, 0.8]

Calculations

Input Gate

i_t = sigmoid(W_i * x_t + U_i * h_(t-1) + b_i)

= sigmoid([[0.1, 0.2], [0.3, 0.4]] * 0.5 + [[1.7, 1.8], [1.9, 2.0]] * [0.2, 0.3] + [0.1, 0.2])

= sigmoid([0.05 + 0.55, 0.1 + 0.65])

= sigmoid([0.6, 0.75])

= [0.55, 0.68]

Forget Gate

f_t = sigmoid(W_f * x_t + U_f * h_(t-1) + b_f)

= sigmoid([[0.5, 0.6], [0.7, 0.8]] * 0.5 + [[2.1, 2.2], [2.3, 2.4]] * [0.2, 0.3] + [0.3, 0.4])

= sigmoid([0.25 + 0.75, 0.35 + 0.85])

= sigmoid([1.0, 1.2])

= [0.73, 0.78]

Cell State Update

c_t = f_t * c_(t-1) + i_t * tanh(W_c * x_t + U_c * h_(t-1) + b_c)

= [0.73, 0.78] * [0.4, 0.5] + [0.55, 0.68] * tanh([[0.9, 1.0], [1.1, 1.2]] * 0.5 + [[2.5, 2.6], [2.7, 2.8]] * [0.2, 0.3] + [0.5, 0.6])

= [0.292, 0.39] + [0.55, 0.68] * tanh([0.45 + 0.7, 0.55 + 0.8])

= [0.292, 0.39] + [0.55, 0.68] * [0.58, 0.66]

= [0.479, 0.63]

Output Gate

o_t = sigmoid(W_o * x_t + U_o * h_(t-1) + b_o)

= sigmoid([[1.3, 1.4], [1.5, 1.6]] * 0.5 + [[2.9, 3.0], [3.1, 3.2]] * [0.2, 0.3] + [0.7, 0.8])

= sigmoid([0.65 + 0.95, 0.75 + 1.05])

= sigmoid([1.6, 1.8])

= [0.82, 0.87]

Hidden State Update

h_t = o_t * tanh(c_t)

= [0.82, 0.87] * tanh([0.479, 0.63])

= [0.82, 0.87] * [0.44, 0.53]

= [0.36, 0.46]

Output

y_t = h_t

= [0.36, 0.46]

This completes the LSTM calculation for one time step.

Here's a small mathematical example for a GRU (Gated Recurrent Unit) network:

Example:

Suppose we have a GRU network with:

Input dimension: 1

Hidden dimension: 2

Input at time t (x_t)

x_t = 0.5

Previous Hidden State (h_(t-1))

h_(t-1) = [0.2, 0.3]

Weight Matrices and Bias Vectors

W_z = [[0.1, 0.2], [0.3, 0.4]]

W_r = [[0.5, 0.6], [0.7, 0.8]]

W_h = [[0.9, 1.0], [1.1, 1.2]]

U_z = [[1.3, 1.4], [1.5, 1.6]]

U_r = [[1.7, 1.8], [1.9, 2.0]]

U_h = [[2.1, 2.2], [2.3, 2.4]]

b_z = [0.1, 0.2]

b_r = [0.3, 0.4]

b_h = [0.5, 0.6]

Calculations

Update Gate

z_t = sigmoid(W_z * x_t + U_z * h_(t-1) + b_z)

= sigmoid([[0.1, 0.2], [0.3, 0.4]] * 0.5 + [[1.3, 1.4], [1.5, 1.6]] * [0.2, 0.3] + [0.1, 0.2])

= sigmoid([0.05 + 0.45, 0.1 + 0.55])

= sigmoid([0.5, 0.65])

= [0.62, 0.66]

Reset Gate

r_t = sigmoid(W_r * x_t + U_r * h_(t-1) + b_r)

= sigmoid([[0.5, 0.6], [0.7, 0.8]] * 0.5 + [[1.7, 1.8], [1.9, 2.0]] * [0.2, 0.3] + [0.3, 0.4])

= sigmoid([0.25 + 0.65, 0.35 + 0.75])

= sigmoid([0.9, 1.1])

= [0.71, 0.75]

Hidden State Update

h~t = tanh(W_h * x_t + U_h * (r_t * h(t-1)) + b_h)

= tanh([[0.9, 1.0], [1.1, 1.2]] * 0.5 + [[2.1, 2.2], [2.3, 2.4]] * ([0.71, 0.75] * [0.2, 0.3]) + [0.5, 0.6])

= tanh([0.45 + 0.55, 0.55 + 0.65])

= tanh([1.0, 1.2])

= [0.58, 0.62]

Hidden State

h_t = (1 - z_t) * h_(t-1) + z_t * h~_t

= (1 - [0.62, 0.66]) * [0.2, 0.3] + [0.62, 0.66] * [0.58, 0.62]

= [0.38, 0.42] + [0.36, 0.41]

= [0.74, 0.83]

This completes the GRU calculation for one time step.

Here are examples of Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) networks:

LSTM Example

Python

# Import necessary libraries

import numpy as np

import pandas as pd

from sklearn.preprocessing import MinMaxScaler

from sklearn.model_selection import train_test_split

from tensorflow.keras.models import Sequential

from tensorflow.keras.layers import LSTM, Dense, Dropout

from tensorflow.keras.callbacks import EarlyStopping

import matplotlib.pyplot as plt

# Generate sample dataset (time series data)

np.random.seed(0)

time_steps = 100

future_pred = 30

data = np.sin(np.linspace(0, 10 * np.pi, time_steps)) + 0.2 * np.random.normal(0, 1, time_steps)

# Plot original data

plt.figure(figsize=(10, 6))

plt.plot(data)

plt.title('Original Data')

plt.show()

# Scale data

scaler = MinMaxScaler()

data_scaled = scaler.fit_transform(data.reshape(-1, 1))

# Split data into training and testing sets

train_size = int(0.8 * len(data_scaled))

train_data, test_data = data_scaled[0:train_size], data_scaled[train_size:]

# Split data into X (input) and y (output)

def split_data(data, future_pred):

    X, y = [], []

    for i in range(len(data) - future_pred):

        X.append(data[i:i + future_pred])

        y.append(data[i + future_pred])

    return np.array(X), np.array(y)

X_train, y_train = split_data(train_data, future_pred)

X_test, y_test = split_data(test_data, future_pred)

# Reshape data for LSTM input

X_train = np.reshape(X_train, (X_train.shape[0], X_train.shape[1], 1))

X_test = np.reshape(X_test, (X_test.shape[0], X_test.shape[1], 1))

# Build LSTM model

model = Sequential()

model.add(LSTM(50, activation='relu', return_sequences=True, input_shape=(future_pred, 1)))

model.add(LSTM(50, activation='relu'))

model.add(Dropout(0.2))

model.add(Dense(1))

# Compile model

model.compile(optimizer='adam', loss='mean_squared_error')

# Early stopping callback

early_stopping = EarlyStopping(patience=5, min_delta=0.001)

# Train model

model.fit(X_train, y_train, epochs=50, batch_size=32, validation_data=(X_test, y_test), callbacks=[early_stopping])

# Make predictions

predictions = model.predict(X_test)

# Plot predictions

plt.figure(figsize=(10, 6))

plt.plot(y_test, label='Actual')

plt.plot(predictions, label='Predicted')

plt.legend()

plt.title('Predictions')

plt.show()

GRU Example

Python

# Import necessary libraries

import numpy as np

import pandas as pd

from sklearn.preprocessing import MinMaxScaler

from sklearn.model_selection import train_test_split

from tensorflow.keras.models import Sequential

from tensorflow.keras.layers import GRU, Dense, Dropout

from tensorflow.keras.callbacks import EarlyStopping

import matplotlib.pyplot as plt

# Generate sample dataset (time series data)

np.random.seed(0)

time_steps = 100

future_pred = 30

data = np.sin(np.linspace(0, 10 * np.pi, time_steps)) + 0.2 * np.random.normal(0, 1, time_steps)

# Plot original data

plt.figure(figsize=(10, 6))

plt.plot(data)

plt.title('Original Data')

plt.show()

# Scale data

scaler = MinMaxScaler()

data_scaled = scaler.fit_transform(data.reshape(-1, 1))

# Split data into training and testing sets

train_size = int(0.8 * len(data_scaled))

train_data, test_data = data_scaled[0:train_size], data_scaled[train_size:]

# Split data into X (input) and y (output)

def split_data(data, future_pred):

    X, y = [], []

    for i in range(len(data) - future_pred):

        X.append(data[i:i + future_pred])

        y.append(data[i + future_pred])

    return np.array(X), np.array(y)

X_train, y_train = split_data(train_data, future_pred)

X_test, y_test = split_data(test_data, future_pred)

# Reshape data for GRU input

X_train = np.reshape(X_train, (X_train.shape[0], X_train.shape[1], 1))

X_test = np.reshape(X_test, (X_test.shape[0], X_test.shape[1], 1))

# Build GRU model

model = Sequential()

model.add(GRU(50, activation='relu', return_sequences=True, input_shape=(future_pred, 1)))

model.add(GRU(50, activation='relu'))

model.add(Dropout(0.2))

model.add(Dense(1))

# Compile model

model.compile(optimizer='adam', loss='mean_squared_error')

# Early stopping callback

early_stopping = EarlyStopping(patience=5, min_delta=0.001)

# Train model

model.fit(X_train, y_train, epochs=50, batch_size=32, validation_data=(X_test, y_test), callbacks=[early_stopping])

# Make predictions

predictions = model.predict(X_test)

# Plot predictions

plt.figure(figsize=(10, 6))

plt.plot(y_test, label='Actual')

plt.plot(predictions, label='Predicted')

plt.legend()

plt.title('Predictions')

plt.show()

Key Differences:

Architecture:

LSTM has three gates (input, output, and forget) and three state vectors (cell state and two hidden states).

GRU has two gates (update and reset) and two state vectors (hidden state).

Computational Complexity:

LSTM is computationally more expensive due to the additional gate and state.

GRU is faster and more efficient.

Performance:

LSTM generally performs better on tasks requiring longer-term dependencies.

GRU performs better on tasks with shorter-term dependencies.

Use Cases:

LSTM:

Language modeling

Text generation

Speech recognition

GRU:

Time series forecasting

Speech recognition

Machine translation

These examples demonstrate basic LSTM and GRU architectures. Depending on your specific task, you may need to adjust parameters, add layers, or experiment with different optimizers and loss functions.

Automated Construction Progress Tracking

Developing an AI-based automated construction progress tracking system for a solar plant is a complex project that involves various components, including computer vision, data analysis, and integration with existing construction management systems. Here's a step-by-step plan through the development process: 

 

 

 

Main features of the application: 

• Work in progress 

• Reality capture 

• Schedule 

• Budget 

• Quality check 

  

Steps we need to follow: 

1. Define Project Objectives and Scope: 

   - Clearly define the goals and objectives of your construction progress tracking system. 

   - Identify the specific metrics and key performance indicators (KPIs) you want to track, such as completion of solar panel installation, infrastructure construction, and overall project progress. 

2. Data Collection and Infrastructure Setup: 

   - Set up the necessary infrastructure for data collection, storage, and processing. This includes setting up cameras and sensors at key construction sites. 

   - Ensure a robust network connection to transmit data to a centralized server. 

3. Computer Vision and Image Data Processing: 

   - Implement computer vision algorithms to analyze images and videos from construction sites. 

   - Develop image recognition models to identify construction equipment, workers, and project milestones. 

   - Use deep learning techniques to detect and track the progress of solar panel installation and other construction activities. 

4. Data Annotation and Training: 

   - Annotate a dataset of images and videos to train your AI models. 

   - Train your models to recognize specific objects, actions, and construction milestones. 

   - Fine-tune the models to improve accuracy. 

5. Real-time Monitoring and Tracking: 

   - Set up real-time monitoring of construction sites using cameras and sensors. 

   - Continuously analyze the data and images to detect anomalies or delays in the construction progress. 

   - Implement algorithms to track and predict construction milestones and timelines. 

6. Data Integration: 

   - Develop APIs and data pipelines to integrate the AI-based progress tracking system with existing construction management software and databases. 

   - Ensure that relevant project data is accessible to project managers and stakeholders. 

7. Dashboard and Reporting: 

   - Create a user-friendly dashboard for project managers and stakeholders. 

   - Provide real-time updates on construction progress, timelines, and KPIs. 

   - Implement reporting and alerting mechanisms for deviations from the planned schedule. 

8. Verification and Validation: 

   - Conduct thorough testing of the AI system to ensure accuracy and reliability. 

   - Validate the system's performance against historical construction project data. 

9. Deployment and Scaling: 

   - Deploy the system at one or more solar plant construction sites. 

   - Monitor system performance and scalability to ensure it can handle multiple projects simultaneously. 

10. Continuous Improvement: 

   - Collect feedback from users and stakeholders to identify areas for improvement. 

   - Continuously refine the AI models and algorithms to enhance accuracy and efficiency. 

   - Stay updated with the latest advancements in computer vision and AI technologies to incorporate improvements. 

11. Maintenance and Support: 

   - Provide ongoing maintenance and support for the system to address issues and ensure it remains operational. 

12. Compliance and Security: 

   - Ensure data privacy and security compliance. 

   - Implement access controls and encryption to protect sensitive project data. 

  

Main technologies will be used: 

• Machine Learning 

• Computer Vision, segment anything from Meta  

• Automated Planning and Scheduling 

 

To monitor the everyday progress of a solar plant, you can use a combination of time-lapse photography, drone imagery, and fixed cameras. Since a single row of a solar plant can be quite long (up to 200 meters), capturing the entire row within a single image may not be feasible. Instead, you may need to take a more segmented approach. Here's how you can capture and process images for progress monitoring: 

  

1. Fixed Cameras: 

   - Install fixed cameras at key vantage points within the solar plant. These cameras can capture high-resolution images of specific areas or sections of the solar plant. 

2. Drones: 

   - Utilize drones equipped with cameras to capture aerial imagery of the entire solar plant. Drones can cover larger areas quickly and provide a top-down view, allowing you to assess progress across rows. 

3. Time-Lapse Photography: 

   - Set up cameras to capture time-lapse images at regular intervals, such as daily or weekly. Time-lapse photography can help create a historical record of construction progress. 

4. Segmentation and Stitching: 

   - Given the long row of the solar plant (up to 200 meters), you may need to capture it in segments or smaller sections. 

   - Use image stitching techniques to combine images from different angles and cameras to create a comprehensive view of the entire row. Software like Adobe Photoshop or specialized stitching software can assist with this. 

5. Data Synchronization: 

   - Ensure that all cameras, drones, and time-lapse cameras are synchronized in terms of time and location. This synchronization is critical for accurate progress tracking. 

6. Image Processing and Analysis: 

   - Develop or deploy the AI-based image analysis system to process the captured images. This system should identify and track the progress of solar panel installation, infrastructure construction, and other relevant activities. 

7. Inference with Model: 

   - When ingesting video data, you can break the video into frames. For a solar plant row spanning 200 meters, you may need to segment the video into shorter clips (e.g., 10-20 meters) to ensure manageable data sizes. 

   - Process each frame or clip with your AI model to detect and track construction progress. 

   - The AI model can analyze each frame, identifying objects, workers, and construction milestones. 

8. Real-time Monitoring: 

   - Implement real-time monitoring and reporting of construction progress. The AI model can provide updates on the status of each segment and the entire row. 

9. Historical Data: 

   - Maintain a database of historical data and images, allowing you to compare the current status with past milestones. 

10. Notifications and Alerts: 

   - Set up notifications and alerts for project managers or relevant stakeholders if the AI system detects anomalies or significant delays. 

11. User Interface: 

   - Create a user-friendly dashboard for stakeholders to access real-time and historical data. The dashboard should display progress metrics, images, and videos. 

  

Capturing the image to detect progress using a drone for daily surveys is cost-prohibitive, you can leverage field or construction personnel to capture video by walking through a row at a time. This approach can still provide valuable data for progress tracking. Here's how you can implement this alternative method: 

1. Assign Field Personnel: 

   - Select and train field personnel responsible for capturing daily or periodic videos of specific rows within the solar plant. Ensure they understand the specific requirements for video capture.

 

2. Video Capture Process: 

   - Field personnel should walk through each designated row while recording video using a smartphone or other recording equipment. 

   - The video should capture the entire row or a significant portion of it, ensuring visibility of key construction activities and milestones. 

3. Data Upload and Management: 

   - Create a structured system for field personnel to upload the captured videos to a central database or cloud storage. 

   - Each video should be tagged with relevant information, such as the date, time, row number, and any other necessary metadata. 

4. Video Segmentation: 

   - As the videos are captured and uploaded, you may need to segment them into smaller clips, especially if a single video covers a long row. 

   - Segmentation helps in efficient processing and analysis. 

5. AI-Based Progress Tracking: 

   - Implement an AI-based image analysis system to process the uploaded videos or video clips. 

   - The AI model should be capable of analyzing the videos, detecting construction activities, and tracking progress milestones. 

6. Real-time Monitoring and Reporting: 

   - Develop a system for real-time monitoring and reporting of construction progress using the data extracted from the videos. 

   - The AI system should provide insights into the status of each row, flagging any anomalies or delays. 

7. User Interface: 

   - Create a user-friendly dashboard for project managers and stakeholders to access progress data, images, and video clips. 

   - The dashboard should display the status of each row and provide historical data for comparison. 

8. Quality Assurance: 

   - Implement a quality assurance process to ensure the videos captured by field personnel are clear, consistent, and meet the necessary standards for analysis. 

9. Feedback and Communication: 

   - Maintain clear communication channels with the field personnel to address any issues, provide guidance, and ensure the data collection process runs smoothly. 

Applications parts: 

1. The backend REST API serverless application can run in Azure Functions. Which will be a batch processing application. A user will upload videos of each row to evaluate the progress of construction and save the data into a common database in the cloud. 

1. Walkthrough, Part 4: Authenticate Python apps with Azure services - Python on Azure | Microsoft Learn 

2. GitHub - Azure-Samples/flask-app-on-azure-functions: A sample to run a Flask app on Azure Functions 

2. Application for construction progress dashboard with all kinds of charts and reports to show the progress, cost and time to complete prediction. 

1. it needs to input each device/module expected setup date and timeline 

2. compare and find the progress and expected completion of the project 

3. show all kinds of chart, graphs, require explaining the progress with help of numpy, pandas, ploty, matplotlib, seaborn 

4. GitHub - eyobofficial/construction-app: A dashboard web app to manage your construction projects 

3. ML segmentation model with https://segment-anything.com/ [meta] which will find the segmentation and all the devices that are there in an image. Which will be generated from the row video. 

1. https://github.com/facebookresearch/segment-anything 

2. after segmentation, each image needs to be inference by each CNN model one after another to identify the object eg. tracker or python clip 

3. we can follow the steps to combine them as described here https://deci.ai/blog/image-segmentation-using-yolo-nas-and-segment-anything/  

4. Time series analysis to automated planning and scheduling optimization 

1. GitHub - jiwidi/time-series-forecasting-with-python: A use-case focused tutorial for time series forecasting with python 

2. An End-to-End Project on Time Series Analysis and Forecasting with Python | by Susan Li | Towards Data Science 

3.