Predicting Energy Consumption for Hybrid Energy Systems toward Sustainable Manufacturing: A Physics-Informed Approach Using Pi-MMoE
Abstract
:1. Introduction
- An in-depth analysis of the production mechanisms in the manufacturing, such as mineral, chemical, and textile industries, has been conducted. A methodology for extracting physical information from a process-oriented perspective has been proposed.
- To address the energy consumption prediction management needs of this manufacturing industry, an MMoE model incorporating gated mechanisms and multi-expert network mechanisms has been introduced. This facilitates the balance between knowledge sharing and the uniqueness of different prediction objectives.
- Building upon a specific textile dyeing and finishing enterprise, physical information was distilled by analyzing its production process. Subsequently, a pi-MMoE model was constructed to achieve multi-objective predictions targeting electricity and steam consumption.
2. Literature Review
2.1. Energy Consumption Forecasting in Manufacturing with Hybrid Energy Supply
2.2. Development and Application of Multi-Task Learning
2.3. Application of Physical Information in Machine Learning
3. Methodology
3.1. Overview of the Physics-Informed Multi-Task Approach
3.2. Extraction of Physical Equation
3.3. The Multi-Gate Mixture-of-Experts Model
3.4. Model Validation and Application
4. Case Study
4.1. Background and Data Status
4.1.1. Industrial Background
4.1.2. Data Description
- -
- Fabric count (pieces): Represents the number of fabric pieces processed during production, helping to measure the scale and efficiency of the production task.
- -
- Weight (kg): The weight of the fabric is an important production parameter that affects the heating and stretching force during the setting process, ensuring the quality and consistency of the final product.
- -
- 1~10# oven temperature (°C): The oven temperatures in each section control the heating phase of the setting process. Precise temperature control is crucial to ensure the setting effect and quality of the fabric.
- -
- 1~8# spindle width (cm): The spindle width determines the width of the fabric being stretched during the setting process, affecting the shape and size of the fabric to ensure the final product meets specifications.
- -
- 1~10# fan speed (expressed as a percentage of the standard wind speed, with the standard wind speed being 20 m/s): Fan speed controls the air circulation and cooling efficiency within the oven, impacting the uniformity of the setting process and the cooling rate of the fabric.
- -
- Machine speed (m/s): The machine speed determines the dwell time of the fabric in the stentering, affecting the heating and cooling time of the fabric, thus influencing the final setting effect.
- -
- Upper feed (cm): The upper feed length determines the tension and position of the fabric as it enters the stentering, directly affecting the stretching and setting of the fabric.
- -
- Workshop temperature (°C): The ambient temperature in the workshop may influence the overall production environment.
4.2. Data Preprocessing
- Standardize the data, transforming it into a distribution with a mean of zero and a standard deviation of one.
- Compute the correlation matrix between variables.
- Employ Principal Component Analysis to determine the factor loading matrix and extract factors.
- Apply orthogonal rotation (Varimax) to the factors to enhance their interpretability.
- Calculate factor scores, estimating the common factors based on original variables.
Algorithm 1: Factor analysis data preprocessing | |
Input: Production data . | |
| |
Output: Latent factor loading matrix | |
The procedure of factor analysis: | |
1: Initialize the data . | |
// represents the size of data, with the value of and | |
2: While do: | |
4: . | |
5: . | |
// and represent the eigenvector matrix and diagonal matrix of . | |
6: . | |
7: . | |
// represents the varimax orthogonal rotation matrix. | |
8: . | |
9: . | |
10: . | |
11: End While. | |
12: where for . | |
13: where for . |
4.3. Evaluation Metrics
4.4. Construction of the Pi-MMoE Model for Textile Dyeing and Printing
Algorithm 2: Pi-MMoE multi-task modeling | |
Input: Temperature of the 10th drying oven . | |
| |
Output: Electric and Steam consumption . | |
The procedure of Pi-MMoE Modeling: | |
1: Initialize the input data . | |
2: While training loss has not converged do: | |
4: . | |
5: for . | |
6: for i . | |
7: for . | |
// The represents the -th element of . | |
8: . | |
// In the model, the and get the value of and . | |
// and represent the predicted value of electric and steam consumption. | |
9: . | |
10: . | |
11: . | |
12: . | |
13: . | |
14: End While. |
4.5. Experimental Setup
4.6. Experimental Results
4.6.1. Effectiveness of Physical Information
4.6.2. Impact of Expert Net
4.6.3. Performance of Multi-Task Modeling
4.7. Discussion
- Physical information is highly valuable in specific production environments. Different models have varying methods and outcomes when utilizing physical information, and selecting the right model is key.
- Choosing the appropriate expert network is a significant challenge in model design. It is vital to ensure the model has enough representational power while preventing overfitting.
- In the field of multi-task learning, guiding model training through inter-task correlations can further enhance model predictive performance, making it a promising research direction.
4.8. Pi-MMoE-Supported Process Optimization to Energy Efficiency
4.8.1. Determinants of Energy Efficiency
4.8.2. Process Optimization for Energy Efficiency
- (a)
- Optimal total energy consumption: This situation arises when the unit price of electricity is on par with the steam.
- (b)
- Prioritize reducing electricity consumption while ensuring overall energy consumption. This situation occurs when the unit price of electricity is higher than the steam.
- (c)
- Prioritize reducing steam consumption while ensuring overall energy consumption: This situation occurs when the unit price of electricity is lower than the steam.
- -
- Oven temperature: By lowering the oven temperature, the energy required for heating is reduced, directly lowering both electricity and steam consumption.
- -
- Spindle width: Adjusting the spindle width ensures more uniform and efficient fabric transfer, reducing energy waste and improving production efficiency.
- -
- Fan speed: Optimizing fan speed significantly reduces motor power consumption while ensuring adequate ventilation and production quality.
- -
- Machine speed: Controlling machine speed optimizes the pace and energy consumption of fabric movement, reducing unnecessary energy waste.
- -
- Total energy consumption strategy: When the unit prices of electricity and steam are comparable, a comprehensive adjustment of all parameters achieves the lowest overall energy consumption.
- -
- Electricity priority strategy: When the unit price of electricity is higher, prioritizing the reduction of electricity consumption through optimized parameter combinations reduces total electricity usage.
- -
- Steam priority strategy: When the unit price of electricity is lower, prioritizing the reduction of steam consumption through precise parameter control reduces steam usage.
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Number of Instances | Production Data Details | Process Data Details |
---|---|---|
1673 | Date, machine number, production type, quantity and weight of fabric, process number, and workshop temperature | 1#~10# oven temperature, 1#~8# spindle width, 1#~10# fan speed, machine speed, and upper feed |
Gate Units | Input Layer | Expert Layer | Tower Layer | Output Layer | |
---|---|---|---|---|---|
Total | 2 | 1 | 6 | 2 | 1 |
Units | 8-4 | 8 | 8-16-4 | 8-4 | 2 |
Model | Item | Details | Input Size | Output Size |
---|---|---|---|---|
MLP | Batch size | 32 | 8 × 1 | 2 × 1 |
Hidden layer | 2 | |||
Hidden neurons | 32-32 | |||
Activation function | Relu | |||
Pi-MLP | Batch size | 32 | ||
Hidden layer | 2 | |||
Hidden neurons | 32-32 | |||
Activation function | Relu | |||
ResNet | Batch size | 32 | ||
Residual block | 2 | |||
Convolution kernel | 3 × 1 | |||
Activation function | Relu | |||
Pi-ResNet | Batch size | 32 | ||
Residual block | 2 | |||
Convolution kernel | 3 × 1 | |||
Activation function | Relu | |||
MMoE | Batch size | 32 | ||
Gate units | 2 | |||
Expert layers | 6 | |||
Expert neurons | 16 | |||
Activation function | Relu | |||
Pi-MMoE | Batch size | 32 | ||
Gate units | 2 | |||
Expert layers | 6 | |||
Expert neurons | 16 | |||
Activation function | Relu |
Model | Item | Details | Input Size | Output Size |
---|---|---|---|---|
Pi-MMoE 2-8 | Expert layers | 2 | 8 × 1 | 2 × 1 |
Expert hidden neurons | 8 | |||
Pi-MMoE 4-8 | Expert layers | 4 | ||
Expert hidden neurons | 8 | |||
Pi-MMoE 6-8 | Expert layers | 6 | ||
Expert hidden neurons | 8 | |||
Pi-MMoE 8-8 | Expert layers | 8 | ||
Expert hidden neurons | 8 | |||
Pi-MMoE 2-16 | Expert layers | 2 | ||
Expert hidden neurons | 16 | |||
Pi-MMoE 4-16 | Expert layers | 4 | ||
Expert hidden neurons | 16 | |||
Pi-MMoE 6-16 | Expert layers | 6 | ||
Expert hidden neurons | 16 | |||
Pi-MMoE 8-16 | Expert layers | 8 | ||
Expert hidden neurons | 16 |
Models | Items | Details | Input Size | Output Size |
---|---|---|---|---|
Pi-MMoE S.T | Gate units | 2 | 8 × 1 | 2 × 1 |
Expert layers | 6 | |||
Expert hidden neurons | 16 | |||
Activation function | Relu | |||
Pi-MMoE S.G M.T | Gate units | 1 | ||
Expert layers | 6 | |||
Expert hidden neurons | 16 | |||
Activation function | Relu | |||
Pi-MMoE M.G M.T | Gate units | 2 | ||
Expert layers | 6 | |||
Expert hidden neurons | 16 | |||
Activation function | Relu |
MLP | Pi-MLP | ResNet | Pi-ResNet | MMoE | Pi-MMoE | |
---|---|---|---|---|---|---|
Electric energy: | ||||||
MAE | 0.17 | 0.12 | 0.20 | 0.19 | 0.21 | 0.10 |
RMSE | 0.21 | 0.15 | 0.24 | 0.23 | 0.25 | 0.12 |
Steam energy: | ||||||
MAE | 0.17 | 0.12 | 0.13 | 0.13 | 0.11 | 0.07 |
RMSE | 0.20 | 0.15 | 0.25 | 0.17 | 0.14 | 0.08 |
Comprehensive: | ||||||
GM-MSE | 0.04 | 0.02 | 0.06 | 0.04 | 0.03 | 0.01 |
Item | p-Value | Different |
---|---|---|
Electric energy: | ||
Pi-MMoE vs. MLP | 0.01 | Yes |
Pi-MMoE vs. Pi-MLP | 0.02 | Yes |
Pi-MMoE vs. ResNet | 0.02 | Yes |
Pi-MMoE vs. Pi-ResNet | 0.04 | Yes |
Pi-MMoE vs. MMoE | 0.39 | No |
Steam energy: | ||
Pi-MMoE vs. MLP | 0.01 | Yes |
Pi-MMoE vs. Pi-MLP | 0.01 | Yes |
Pi-MMoE vs. ResNet | 0.04 | Yes |
Pi-MMoE vs. Pi-ResNet | 0.02 | Yes |
Pi-MMoE vs. MMoE | 0.75 | No |
Pi-MMoE 2-8 | Pi-MMoE 4-8 | Pi-MMoE 6-8 | Pi-MMoE 8-8 | Pi-MMoE 2-16 | Pi-MMoE 4-16 | Pi-MMoE 6-16 | Pi-MMoE 8-16 | |
---|---|---|---|---|---|---|---|---|
Electric energy: | ||||||||
MAE | 0.12 | 0.11 | 0.16 | 0.10 | 0.12 | 0.10 | 0.10 | 0.10 |
RMSE | 0.14 | 0.13 | 0.15 | 0.12 | 0.14 | 0.12 | 0.12 | 0.11 |
Steam energy: | ||||||||
MAE | 0.09 | 0.09 | 0.07 | 0.07 | 0.09 | 0.07 | 0.07 | 0.07 |
RMSE | 0.11 | 0.11 | 0.08 | 0.08 | 0.11 | 0.09 | 0.08 | 0.09 |
Comprehensive: | ||||||||
GM-MSE | 0.014 | 0.014 | 0.014 | 0.014 | 0.01 | 0.014 | 0.01 | 0.01 |
Items | p-Value | Different |
---|---|---|
Electric energy: | ||
Pi-MMoE 6-16 vs. Pi-MMoE 2-16 | 0.02 | Yes |
Pi-MMoE 6-16 vs. Pi-MMoE 4-16 | 0.00 | Yes |
Pi-MMoE 6-16 vs. Pi-MMoE 8-16 | 0.00 | Yes |
Pi-MMoE 6-16 vs. Pi-MMoE 6-8 | 0.55 | No |
Steam energy: | ||
Pi-MMoE 6-16 vs. Pi-MMoE 2-16 | 0.00 | Yes |
Pi-MMoE 6-16 vs. Pi-MMoE 4-16 | 0.00 | Yes |
Pi-MMoE 6-16 vs. Pi-MMoE 8-16 | 0.00 | Yes |
Pi-MMoE 6-16 vs. Pi-MMoE 6-8 | 0.19 | No |
Pi-MMoE S.T. | Pi-MMoE S.G. M.T. | Pi-MMoE M.G. M.T. | |
---|---|---|---|
Electric energy: | |||
MAE | 0.16 | 0.14 | 0.10 |
RMSE | 0.19 | 0.17 | 0.12 |
Steam energy: | |||
MAE | 0.15 | 0.11 | 0.07 |
RMSE | 0.17 | 0.13 | 0.08 |
Comprehensive: | |||
GM-MSE | 0.04 | 0.02 | 0.01 |
Items | p-Value | Different |
---|---|---|
Electric energy: | ||
Pi-MMoE M.G. M.T. vs. Pi-MMoE S.T. | 0.00 | Yes |
Pi-MMoE M.G. M.T. vs. Pi-MMoE S.G. M.T. | 0.02 | Yes |
Steam energy: | ||
Pi-MMoE M.G. M.T. vs. Pi-MMoE S.T. | 0.01 | Yes |
Pi-MMoE M.G. M.T. vs. Pi-MMoE S.G. M.T. | 0.00 | Yes |
Production Information | ||||
---|---|---|---|---|
Date | 6 May 2023 | |||
Production details | Type: Y6260; quantity: 94; weight: 2379.5 kg | |||
Workshop temperature | 28 °C | |||
Process No. | 06735-1-3 | |||
Strategies | Total energy | Reduce electricity | Reduce steam | |
Decision coefficients | = 0.5, = 0.5 | = 0.75, = 0.25 | = 0.25, = 0.75 | |
Item | Original Details | Optimized Details | ||
1~10# Oven temperature /°C | 180 | 173 | 174 | 171 |
1~8# spindle width /cm | [150, 150, 150, 150, 150, 150, 150, 150] | [157, 157, 157, 157, 157, 157, 157, 157] | [157, 157, 157, 157, 157, 157, 157, 157] | [157, 157, 157, 157, 157, 157, 157, 157] |
1~10# fan speed /% | [98, 98, 98, 98, 98, 98, 95, 95, 95, 95] | [92, 92, 92, 92, 93, 92, 92, 92, 93, 98] | [89, 89, 89, 89, 90, 89, 89, 89, 90, 92] | [94, 94, 94, 94, 96, 94, 94, 94, 96, 99] |
Electric consumption/kW·h | 256 | 238 (↓ 1 7.03%) | 233 (↓8.98%) | 241 (↓5.86%) |
Steam consumption /t | 1.50 | 1.40 (↓6.67%) | 1.43 (↓4.67%) | 1.37 (↓8.67%) |
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Share and Cite
Yuan, M.; Liu, J.; Chen, Z.; Guo, Q.; Yuan, M.; Li, J.; Yu, G. Predicting Energy Consumption for Hybrid Energy Systems toward Sustainable Manufacturing: A Physics-Informed Approach Using Pi-MMoE. Sustainability 2024, 16, 7259. https://doi.org/10.3390/su16177259
Yuan M, Liu J, Chen Z, Guo Q, Yuan M, Li J, Yu G. Predicting Energy Consumption for Hybrid Energy Systems toward Sustainable Manufacturing: A Physics-Informed Approach Using Pi-MMoE. Sustainability. 2024; 16(17):7259. https://doi.org/10.3390/su16177259
Chicago/Turabian StyleYuan, Mukun, Jian Liu, Zheyuan Chen, Qingda Guo, Mingzhe Yuan, Jian Li, and Guangping Yu. 2024. "Predicting Energy Consumption for Hybrid Energy Systems toward Sustainable Manufacturing: A Physics-Informed Approach Using Pi-MMoE" Sustainability 16, no. 17: 7259. https://doi.org/10.3390/su16177259