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Indoor occupancy estimation from carbon dioxide concentration

Chaoyang Jiang, Mustafa K. Masood, Yeng Chai Soh, Hua Li

arXiv:1607.05962v1eess.SYcs.LG

TL;DR

The paper addresses real-time indoor occupancy estimation from CO2 measurements despite noisy spikes and the limitations of existing approaches. It identifies a dynamic occupancy estimator with FS-ELM, uses smoothing strategies available in real time, and evaluates the result with x-tolerance accuracy, reaching up to 94% accuracy with a tolerance of four occupants.

  • Problem

    Existing occupancy-estimation approaches have limitations, while measured CO2 data can contain spikes that negatively affect estimation and globally smoothed data is unavailable in real time.

  • Method

    The paper directly identifies a dynamic occupancy estimator from CO2 measurements using FS-ELM, applies CO2 smoothing with a locally smoothed real-time alternative, and introduces x-tolerance accuracy.

  • Results

    94% x-tolerance accuracy is achieved with a tolerance of four occupants.

  • Takeaways & Limitations

    FS-ELM improves RMSE, while pre-smoothing CO2 data improves occupancy detection in the tested office-room setting.

Abstract

from arXiv · show

This paper presents an indoor occupancy estimator with which we can estimate the number of real-time indoor occupants based on the carbon dioxide (CO2) measurement. The estimator is actually a dynamic model of the occupancy level. To identify the dynamic model, we propose the Feature Scaled Extreme Learning Machine (FS-ELM) algorithm, which is a variation of the standard Extreme Learning Machine (ELM) but is shown to perform better for the occupancy estimation problem. The measured CO2 concentration suffers from serious spikes. We find that pre-smoothing the CO2 data can greatly improve the estimation accuracy. In real applications, however, we cannot obtain the real-time globally smoothed CO2 data. We provide a way to use the locally smoothed CO2 data instead, which is real-time available. We introduce a new criterion, i.e. $x$-tolerance accuracy, to assess the occupancy estimator. The proposed occupancy estimator was tested in an office room with 24 cubicles and 11 open seats. The accuracy is up to 94 percent with a tolerance of four occupants.

I. INTRODUCTION

The paper develops a real-time, non-intrusive occupancy estimator from CO2 measurements to address limitations of camera-, device-, and sensor-based approaches. It combines a dynamic occupancy model, FS-ELM identification, CO2 smoothing, and x-tolerance accuracy, then evaluates the method in a large office room.

  • Motivation: Camera methods can estimate occupants accurately but require expensive hardware and raise privacy concerns, while terminal-based methods miss occupants not using the required devices.The reviewed terminal-based methods include keyboards, mice, smartphones, and RFID tags.
  • Motivation: CO2 sensors enable non-intrusive, non-terminal-based occupancy estimation without additional hardware because they are already available in standard HVAC systems.The paper contrasts this approach with intrusive camera systems and terminal-based methods that raise cost, privacy, security, or coverage concerns.
  • Contributions: The proposed estimator directly models current occupancy from CO2 measurements and past estimated occupancy, avoiding the deconvolution process used in prior dynamic-model work.The prior method achieved accuracy up to 88.8% with a five-minute delay in a room with at most four occupants.
  • Evaluation: The method was tested in an office room with 24 cubicles and 11 open seats, addressing a setting larger than those commonly studied in earlier work.The authors state that most prior methods dealt with very few occupants.
  • Contributions: FS-ELM modifies standard ELM with a feature layer and scaled random feature-to-hidden weights while retaining computational efficiency.The paper presents FS-ELM as more effective for identifying the occupancy estimator and notes that its application can extend to other problems.
  • Contributions: CO2 smoothing improves estimation, and locally smoothed data provides a real-time alternative when globally smoothed data is unavailable.The paper also describes a way to remove accumulated error caused by replacing global smoothing with local smoothing.

II. INDOOR OCCUPANCY ESTIMATION FROM CO2 DATA

The paper formulates occupancy estimation as a regression problem driven by recent CO2, occupancy, and ventilation information, then identifies the estimator using a feature-scaled ELM. FS-ELM addresses saturation and scale imbalance that can limit standard ELM regression.

  • Occupancy model: The occupancy estimator predicts current occupants from recent CO2 concentrations, past occupancy numbers, and ventilation levels over a time horizon.The estimator is a regression model between the constructed input vector x_k and current occupant number o_k.
  • Occupancy model: Directly identifying the occupancy estimator avoids truncation and model-identification errors associated with the prior deconvolution strategy.The paper motivates direct identification because deconvolution can suffer from both truncation errors and errors in the identified CO2 dynamic model.
  • Standard ELM: ELM is selected for its simplicity, computational efficiency, and flexibility in solving the estimator’s regression problem.Standard ELM randomly generates input-to-hidden weights without tuning, which makes training computationally efficient.
  • Standard ELM: Standard ELM can produce poor regression estimates when sigmoid hidden neurons saturate at 0 or 1 and therefore cannot distinguish inputs producing |z_ki| > 5.Using more hidden neurons may improve approximation but increases training cost.
  • Standard ELM: CO2 concentration can overwhelm occupancy and ventilation inputs because it is measured in hundreds to thousands of ppm while the other values are much smaller.This imbalance can adversely affect regression-model training when the input-to-hidden weights are randomly generated.
  • FS-ELM: FS-ELM adds a feature layer and scales the random feature-to-hidden weights to improve performance while retaining standard ELM computational efficiency.The proposed structure is shown in Fig. 3.

B. The feature layer of the FS-ELM

The FS-ELM feature layer preprocesses the occupancy-estimation inputs into CO2 and occupancy-related features designed to represent temporal behavior before hidden-layer mapping.

  • Feature construction: The feature layer preprocesses input data before the hidden layer and uses selected features motivated by prior occupancy-estimation studies.The feature-layer vector includes CO2-derived features together with past occupancy information.
  • Feature construction: The CO2 feature set includes the past CO2 sequence, integrated first-order CO2 differences, and first-order CO2 differences, collectively called the PID of CO2 data.The integrated difference uses a larger sampling time than the ordinary first-order difference.
  • Feature construction: The feature-layer dimension is nf = 5l − s + 3.The feature vector is denoted y_k, and the construction combines the selected CO2 features with past occupancy information.

C. The hidden layer of the FS-ELM

FS-ELM keeps the standard ELM hidden and output structure after feature preprocessing but replaces the random feature-to-hidden matrix with a scaled matrix designed to control activation inputs.

  • Hidden layer: The feature layer acts as preprocessing, while the feature, hidden, and output layers otherwise retain the standard ELM structure.This separates feature construction from the subsequent hidden-layer and output-layer processing.
  • Hidden layer: FS-ELM uses a feature-to-hidden weight matrix W2 = RS, where R is random and S is a diagonal scaling matrix.The scaling matrix is designed to scale hidden-layer activation inputs and satisfy the method’s activation-range requirement.
  • Hidden layer: The hidden-layer activation function is the sigmoid function.The paper identifies h(·), the ELM random feature mapping, as the sigmoid function.

D. FS-ELM training

FS-ELM extends ELM with feature scaling so different input features have balanced influence on hidden neurons, while retaining efficient training. Its scale matrix is tuned from training data, and output weights are solved by regularized least squares.

  • Feature scaling: Equal feature scales let the much larger CO2 values overwhelm the other four features, making those features insignificant.The scale matrix balances feature influence and constrains hidden-layer inputs to a proper range.
  • Feature scaling: FS-ELM adds a feature layer with a scaled random feature-to-hidden weight matrix to improve occupancy regression.The scalable parameters adjust the influence of the five features on the hidden neurons.
  • Training procedure: The training process tunes the scale matrix and hidden-to-output weights while random matrices and biases remain fixed after generation.The scalable parameters are selected through cross validation, and β is obtained from the hidden-layer output matrix.
  • Training procedure: Regularization is added to the least-squares solution to improve generalization and robustness.The regularized output-weight solution uses γ as a regularization parameter.
  • Computational cost: FS-ELM retains the computational efficiency of standard ELM because training’s main cost is solving an inverse matrix.The output weights are computed using the hidden-layer matrix and a least-squares procedure.

IV. SMOOTHED CO2 DATA FOR OCCUPANCY ESTIMATION

Raw CO2 measurements contain spikes that do not represent whole-room concentration, so the paper smooths CO2 data before identifying the occupancy estimator. The smoothed-data estimator outperforms the raw-data estimator, although global smoothing is not real-time available.

  • Motivation: Measured CO2 concentration suffers from spikes caused by noise, irregular air movement, and occupants approaching the sensor.These spikes prevent the measurement at one location from reflecting the CO2 level of the whole indoor space.
  • Real-time use: Global smoothing requires complete CO2 data, so it is unavailable in real time when future measurements have not yet been collected.The paper therefore motivates replacing globally smoothed data with locally smoothed data during estimator use.
  • Global smoothing: The smoothed CO2 signal is obtained by minimizing an energy function that balances fidelity to measurements against smoothing.Increasing λ produces more smoothing, and the resulting tridiagonal system can be solved in O(N) operations.
  • Estimator identification: Training FS-ELM with smoothed CO2 data produces an occupancy estimator that outperforms one trained directly on raw measurements.The paper reports this comparison as an experimental result.

B. Occupancy estimation from locally smoothed CO2 data

Because global smoothing uses future data, the estimator must operate with locally smoothed CO2 measurements. The proposed procedure recomputes past occupancy levels without reusing the previous estimate, preventing error transmission and accumulation.

  • Real-time constraint: Global smoothing cannot be used online because the entire day’s CO2 data, including future measurements, is unavailable in real time.Only current and past CO2 measurements are available during estimator use.
  • Local smoothing: Locally smoothed CO2 data nearly coincides with globally smoothed data except near the current-time endpoint.The endpoint difference is small compared with the magnitude of the spikes.
  • Estimator mismatch: Directly using the globally trained estimator with local smoothing creates a mismatch between the data used for training and the real-time data used online.The paper identifies this mismatch as one of two problems with direct use.
  • Online procedure: The online procedure evaluates local smoothing and estimates all occupancy levels in the current horizon at each sampled time.The current occupancy estimate is taken from the endpoint of that recomputed horizon.
  • Error control: The procedure avoids accumulated error because the current estimate does not use the previous estimated occupancy level.Consequently, estimation error cannot be transmitted through successive estimates.
  • Initialization: The estimator can be reset at midnight with an initial occupancy state of zero.This provides the stated initialization rule for daily operation.

A. Statement of the experiment

The experiment evaluates occupancy estimators using multiple error and detection criteria, including a new tolerance-based accuracy measure. It uses 30 weekdays of video-derived occupancy ground truth from an office laboratory with 24 cubicles and 11 open seats.

  • Test bed: The test bed is a 9.3m × 20m office containing 24 cubicles and 11 open seats.Five corner seats are rarely occupied.
  • Ground truth: Ground truth occupancy is calculated from manually counted entrances and exits in synchronized one-minute video intervals.Computer vision identifies relevant minutes, after which manual counts determine occupancy levels.
  • Ground truth: Thirty weekdays of occupancy data were collected and used as the ground truth.The calculated occupancy levels were zero after 11:30 pm on all 30 days, indicating near-exact collection.
  • Performance indices: The evaluation uses RMSE, false positive rate, false negative rate, false detection rate, and x-tolerance accuracy.These indices cover estimation magnitude, occupancy detection errors, and tolerance-bounded occupancy estimates.
  • Performance indices: Exact accuracy is less informative for larger rooms because small numerical differences may not change an HVAC or lighting decision.The paper gives an estimate of 21 versus an actual occupancy of 20 as an example.
  • Performance indices: x-tolerance accuracy reports the percentage of estimates whose occupancy errors are at most x.Ordinary accuracy is the special case x = 0, and x should be selected for the application.

D. The parameters setting and results

The evaluation used 30 days of office data, with 25 days for training and five for testing, and compared ELM-based estimators under different CO2 preprocessing conditions. FS-ELM reduced fluctuation-sensitive errors, while smoothing improved detection and enabled up to 94% accuracy within four occupants.

  • The parameters setting: 30 days of office data were collected: 25 days trained the estimators and five days tested them.Random matrices and training parameters were specified for ELM and FS-ELM experiments.
  • Results: FS-ELM improved occupancy-curve tracking over standard ELM, whose estimates showed serious fluctuations and jumps after ventilation was turned off.The standard ELM was sensitive to CO2 noise, while FS-ELM reduced the influence of CO2 scale relative to the venting-level feature.
  • Results: Global CO2 smoothing produced the best result among the four estimators, but real-time use required locally smoothed data because future measurements were unavailable.The locally smoothed testing results were quite similar to those obtained with globally smoothed data.
  • Results: FS-ELM improved RMSE relative to standard ELM, while CO2 smoothing greatly improved FDR; FPR and FNR indicated more false detections when the room was empty.These conclusions were based on RMSE, FDR, FPR, and FNR across the five testing days.
  • Results: 0-tolerance accuracy was no more than 50%, whereas three- and four-tolerance accuracy reached 89% and 94%, respectively.Exact daytime occupant counts remained challenging, but three to four occupants’ error was reported as insignificant for air-conditioning and lighting decisions in the tested office.

VI. CONCLUSIONS

The proposed occupancy estimator models occupancy from CO2 data, venting level, and past occupancy, using FS-ELM and locally smoothed measurements for real-time operation. FS-ELM improves RMSE performance, while CO2 pre-smoothing enhances occupancy detection.

  • The estimator represents occupancy as a discrete-time dynamic model driven by CO2 data, venting level, and past occupancy over a moving horizon.
  • FS-ELM adds a feature layer and scales the random hidden-layer weights while retaining standard ELM computational efficiency.
  • Pre-smoothing CO2 data improves occupancy-estimation results, and a correction method enables locally smoothed data to replace unavailable globally smoothed data in real time.
  • FS-ELM greatly improves performance in terms of RMSE, while CO2 pre-smoothing greatly enhances occupancy detection.
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