11institutetext: Telecooperation Office, Karlsruhe Institute of Technology,
Karlsruhe, Germany 11email:
yhuang, hzhao, zhou, riedel<EMAIL_ADDRESS>

# Standardizing Your Training Process for Human Activity Recognition Models –
A Comprehensive Review in the Tunable Factors††thanks: Supported by the
Ministry of Science, Research and the Arts Baden-Wuerttemberg as part of the
SDSC-BW and by the Carl-Zeiss-Foundation as part of ”stay young with robots”
(JuBot) project.

Yiran Huang  0000-0003-3805-1375 Haibin Zhao  0000-0001-7018-1159 Yexu Zhou
0000-0002-8866-7998 Till Riedel  0000-0003-4547-1984 Michael Beigl
0000-0001-5009-2327

###### Abstract

In recent years, deep learning has emerged as a potent tool across a multitude
of domains, leading to a surge in research pertaining to its application in
the Wearable Human Activity Recognition (WHAR) domain. Despite the rapid
development, concerns have been raised about the lack of standardization and
consistency in the procedures used for experimental model training, which may
affect the reproducibility and reliability of research results. In this paper,
we provide an exhaustive review of contemporary deep learning research in the
field of WHAR and collate information pertaining to the training procedure
employed in various studies. Our findings suggest that a major trend is the
lack of detail provided by model training protocols. Besides, to gain a
clearer understanding of the impact of missing descriptions, we utilize a
control variables approach to assess the impact of key tunable components
(e.g., optimization techniques and early stopping criteria) on the inter-
subject generalization capabilities of HAR models. With insights from the
analyses, we define a novel integrated training procedure tailored to the WHAR
model. Empirical results derived using five well-known WHAR benchmark datasets
and three classical HAR model architectures demonstrate the effectiveness of
our proposed methodology: in particular, there is a significant improvement in
macro F1 Leave-One-Subject-Out (LOSO) Cross-Validation (CV) performance.

###### Keywords:

human activity recognition deep learning model.

##  1 Introduction

Wearable Human Activity Recognition (WHAR) is a process that aims to classify
human actions within a specific temporal boundary based on measurements, e.g.,
acceleration, rotation speed, and geographical coordinates, gathered from
personal digital devices [23]. It is central to numerous applications and
services. For instance, in the smart homes [3], accurately detecting a user’s
activity, such as watching television, can enable the automation of derivative
tasks like adjusting room light levels. Similarly, in industrial manufacturing
[5], recognizing a worker’s current task could aid in suggesting sequential
actions for workflow optimization. In the context of road safety [29],
identifying a driver’s present driving behavior or mental states can catalyze
measures to improve road safety. These applications place high-performance
demands on a WHAR system, necessitating the guarantees of sufficient data and
high-performance models.

Wearable technology has experienced significant growth in recent years, with
nearly 500 million units shipped globally by the end of 2022, a 500% increase
from the 82 million units shipped in 2016. Smartwatches are projected to be
the most popular, accounting for 216 million units in 2022. Smart trackers and
glasses follow, with 105 million and 32 million units, respectively. Equipped
with various sensors, these devices offer advantages such as unobtrusive
continuous data collection, direct user contact, and long battery life.
Consequently, they provide detailed insights into human behavior, making
wearables a key platform for developing applications that automatically
recognize human activity.

According to Google Scholar 111https://scholar.google.com., from 2021 to the
present, a total of 1,660 academic articles have contained the keywords ”human
activity recognition” and ”neural networks” in their titles.

Although these factors have contributed to the rapid growth of WHAR, they also
pose challenges in terms of reproducing recent work and benchmarking research.
There is a noticeable lack of attention given to explicating the process by
which experimental models are trained. The training process of a model,
encompassing the trajectory of model development from initialization to
gaining expertise in a specific task, plays a pivotal role in determining the
model’s final performance.

A comprehensive description of the training process should include the
following components: Dataset Description, Model Parameters Setting if
present, Data Preprocessing, Batch Size and Maximum Epoch Setting, Optimizer
Setting, Learning rate strategy, Early stopping strategy, Final model
selection strategy, Validation&Test setting, Additional details.

By comprehensively articulating each stage of the training process, the
intention of the training process description is to provide the reader with
the ability to accurately replicate the experimental result described in the
publication. Such documentation reinforces the transparency and integrity of
the research, elements that are paramount in the field of deep learning
science.

Nonetheless, our analysis points out that while nearly all publications
deliver comprehensive details about dataset descriptions, model parameters
setting, data preprocessing, and validation and test settings, there is a
notable lack of exhaustive detail in other aspects.

Until now, the majority of review articles in the realm of WHAR have mainly
concentrated on outlining various machine learning and deep learning
architectures, with an emphasis on model design. Contrary to this trend, our
research pivots its focus towards a comprehensive analysis of the model
training process in the context of WHAR. To the best of our knowledge, this
survey stands as a pioneering effort specifically targeting descriptions of
the model training process. Through this exploration, we endeavor to shed
light on the current state of model training process narratives in the
relevant literature and proffer recommendations to guide future scholarly
pursuits in this domain.

The key contributions of our work can be summarized below:

  * •

To the best of our knowledge, we are the first in the WHAR field to write a
review that focuses on the model training procedure in various research
papers.

  * •

This study delivers insights into how models have been trained in recent
years. It identifies prevailing issues about model training in the field and
highlights the potential consequences of these problems using control
variables.

  * •

In response to these identified issues, we propose a countermeasure and
provide experimental evidence of its efficacy.

  * •

We are releasing the proposed training procedure as an open-source package to
aid in further research in this field.

Table 1: Summarize of the hyperparameters and the corresponding range in model training procedure. Parameter |  Range
---|---
Optimizer |  {sGD [20], ADAM [13], Adadelta [27], Rmsprop}
Learning Rate |  [$1e-1$, $1e-5$]
Weight Decay |  [$1e-1$, $1e-8$]
Scheduler |  {Step [25], LRPlateau [22], Cos [16], Cos+restart [16]}
Scheduler Base |  {Train Loss, Validation Loss, Train Metric, Validation Metric}
Scheduler Patience (epoch) |  [1, 100]
Batch Size |  [16, 512]
Maximum Epoch |  [10, 1500]
Early Stopping |  {Yes, No}
Early Stopping Base |  {Train Loss, Validation Loss, Train Metric, Validation Metric}
Early Stopping Patience (epoch) |  [1,100]
Model Selection Base |  {Last, Train Loss, Validation Loss, Train Metric, Validation Metric}

##  2 Search Strategy

We followed Preferred Reporting Items for Systematic review and Meta-Analysis
Protocols (PRISMA-P) to select relevant and important articles for our
research target. We completed this search using two protocols: the search
protocol and the three-level exclusion protocol.

Search Protocol: We utilized Google Scholar, a free academic search engine
provided by Google, as our search platform. It provides an extensive coverage
of academic literature across numerous disciplines worldwide, such as journal
articles, theses, conference papers, and more. Its database is regularly
updated, ensuring access to the most recent academic literature. Google
Scholar supports keyword-based searches to retrieve related articles. In
alignment with our research goals, we initially used the following three
keyword sets for our exploration: (”Human Activity Recognition” OR ”HAR”),
(”Machine learning” OR ”Deep learning” OR ”Neural network”), and (”Wearable”
OR ”Smartphone” OR ”Smartwatch” OR ”Smartglasses” OR ”Smartband”), combined
with the platform’s limited search statements. In light of our objective to
analyze the latest developments, we limited the search time frame to 2021
through June 2023. Through this procedure, we sourced a total of 4,960
articles.

Three-Level Exclusion Protocol: We prioritized relevance and ranked papers by
their impact and subsequently excluded duplicates, non-English articles, non-
conference/journal papers, and those lacking references. We filtered out
articles whose titles did not align with our research purpose. This initial
inspection helped us narrow down to 274 articles. By reading the abstracts of
these 274 articles, we removed survey articles and those that focused on other
types of Human Activity Recognition (HAR) tasks. The second filtering phase
yielded 208 papers. On downloading these papers and swiftly reviewing their
contents, we discarded those primarily focusing on machine learning models,
data collection, and data processing. The third and final filtering round
culminated in a total of 102 papers.

##  3 Observation

In deep learning, beyond the inherent model parameters optimized using
gradient descent, several hyperparameters critically influence a model’s
performance. These include the number of layers, kernel sizes, and training
aspects like optimizer selection and batch size. These hyperparameters are not
directly learned through training but profoundly affect the model’s structural
complexity, training speed, and overall efficacy.

The description of the training process in a research paper is essentially a
record of the values taken for these parameters. It ensures that the entire
training process of the model is unambiguous. Table 1 summarizes the
hyperparameters that describe the training process, along with their common
ranges within the WHAR domain as derived from 102 studied papers.

For a specific task, hyperparameter tuning aims to identify the optimal
configuration of hyperparameters leading to the best model performance e.g.
through Bayesian Optimization [26], reinforcement learning [9] or Monte Carlo
[8, 7]. However, as demonstrated in Table 1, the search space for training
model hyperparameters is vast. It leads to substantial computational costs
associated with hyperparameter tuning, especially for tasks like WHAR that
involve large datasets and complex feature extraction using complex models.
Individual model training on the classic oppo [2] dataset can take
approximately one hour on Tesla P100 222The performance is tested with
https://colab.research.google.com/.. Performing systematic hyperparameter
searches incurs significant time and computational resource expenses.
Furthermore, considering typical limitations in paper length and the focus of
WHAR-related papers on introducing new model structures, algorithms, or
theories, hyperparameter tuning is generally not the primary focus. Among the
102 papers we analyzed, only 16 of them (15.7%) involved hyperparameter
tuning.

We observe that all these works only explored a subset of the hyperparameter
space. Most concentrated on seeking for the learning rate and batch size,
followed by the number of epochs and the choice of optimizer. There is a lack
of exploration in other hyperparameter dimensions. Additionally, we found that
the results of the search efforts were relatively consistent regarding
optimizer and learning rate. All searches pertaining to the optimizer
ultimately converged on selecting the Adam optimizer [13]. The majority of
chosen learning rates were around $1e-3$, accounting for $64.3\%$ of similar
searches. Epoch values mostly centered around $60$. Batch size results were
polarized, with half of the studies selecting a size of $64$, while the other
half opted for batch sizes above $400$. This apparent inconsistency in the
search results further emphasizes the significance of hyperparameters. It
underscores that the required hyperparameters can vary significantly based on
differences in models and data.

Apart from the $16$ articles that engaged in hyperparameter tuning, the
remaining $86$ articles addressed the potential adverse effects of neglecting
hyperparameter tuning through various strategies. Some adopted parameter
settings from similar works, while the majority rely on empirical choices [30,
10]. Figure 1 illustrates the hyperparameter setting made by these articles in
terms of the four mentioned parameters. Similar to the tuning results, these
studies also predominantly favored the Adam optimizer [13]. Concerning
learning rates, in addition to $1e-3$, $1e-4$ was also a popular choice. The
setting of the epoch number deviated from the tuning results. Most of the
works leaned towards larger epoch values. This trend could be attributed to
the application of techniques like early stopping. In early stopping
scenarios, even if a large number of epochs is set, training can be terminated
ahead of time if specific conditions are met. For instance, if the validation
loss ceases to decrease, training can halt prematurely. These strategies aim
to mitigate the negative impact of neglecting exhaustive hyperparameter
optimization. While they might not yield the optimal performance, they offer a
practical approach given the resource constraints, limited paper space, and
the specific focuses of the papers in the WHAR domain.

Additionally, we observed in Figure 1 that the ”none” category has a high
occurrence rate across all plots. This signifies that, using batch size as an
example, in these papers, 45% of them did not provide a description of the
batch size. This indicates an incompleteness in the descriptions of their
model training process. This scenario is likewise seen in other hyperparameter
plots.

Figure 2 presents a summary of the descriptions related to parameter
schedulers across all reviewed papers. It was found that 81% of the articles
lacked descriptions about schedulers. Moreover, only 6% of the articles
described early stopping procedures, and only 9% outlined the final model
selection process.

Figure 1: Distribution on the four hyperparameters Optimizer, Learning Rate,
Batch Size, and Epoch across all reviewed papers. ’none’ indicates that there
is no corresponding description in the paper.

Intuitively, it is clear that challenges due to descriptive deficiencies can
significantly affect the reliability and reproducibility of the corresponding
articles, underscoring the need for a standardized and comprehensive
description of model training. However, the actual strength of the impact of
the parameters describing the model training process, for instance, optimizer
settings (type, learning rate, weight decay), early stopping strategies and
model selection strategies, on the WHAR model end performance remains an open
question, which is discussed in the next section.

##  4 Control-Variates Analysis

This section aims to investigate the independent impact of the aforementioned
factors on the final model performance in WHAR context. To achieve this, we
employ the control-variates method and run experiments with CNNLSTM [17] model
on the HAPT [19] dataset. The baseline training procedure is derived from the
collected papers by identifying the most frequently utilized hyperparameters
(as described in section 3) in the training procedure. Specifically, an Adam
optimizer [13] is employed with an initial learning rate set at $1e-3$ and no
weight decay. Cross-entropy is selected as the loss function, along with batch
training set to a batch size of $64$. The maximum number of epochs is capped
at $60$. A step scheduler is also utilized to reduce the learning rate by a
factor of $0.1$ every $10$ epochs. For early stopping, we use a $10$-epoch
patience also based on validation loss. The test model selected runs on the
least validation loss post-training. Figure 3 visualizes the validation loss
during the training in control-variates experiment for hyperparameter:
optimizer, learning rate, weight decay and batch size.

Figure 2: Distribution of choices for scheduler hyperparameters across all
reviewed papers.

Figure 3(a) depicts the impact of diverse optimizers (i.e., sGD [20], Adagrad
[4], and Adam [13]) on model training. Our analysis finds notable variance in
results across these optimizers. Of the three, Adam [13] yields the best
performance. Conversely, sGD [20] does not converge due to its hyperparameter
sensitivity and inappropriate initialization.

Figure 3(b) illustrates the effect of different initial training rates.
Notably, although the baseline Adam optimizer [13] can adaptively adjust the
step size, which is almost equivalent to adjusting the learning rate, the
initial learning rate still plays a crucial role in the model training. In
particular, setting an improper initial learning rate may hinder the model
from converging (e.g., the black curve), leading to suboptimal performance. In
addition, the best model performance is achieved by setting the initial
learning rate $1e-3$.

Despite the strong capability of weight decay for improving model
generalization in other domains [15, 6], Figure 3(c) draws a different
conclusion in WHAR domain. We can observe that the utilization of different
weight decays does not significantly influence the validation loss. An
excessive weight decay may even increase the validation loss, conversely,
setting the weight to $1e-4$ seems to facilitate a more stable training
process.

Figure 3: Validation loss during model training in control-variates
experiment.

Figure 3(d) summarizes the validation loss with different batch sizes.
Consistent with the conclusion from another independent work [12], a smaller
batch size leads to the better model generalization. However, as reported in
Figure 1, it is not a common option in recent WHAR articles.

Figure 4: Mean and standard deviation of the validation loss (left) and macro
F1 score (right) of the models trained on HAPT dataset.

Figure 4 depicts the validation loss and macro F1 score over the epoch during
the training on HAPT [19] dataset. The solid line represents the mean F1 score
w.r.t. subjects, while the shading indicates the corresponding variance. Our
analysis reveals that the validation loss decreases gradually and reaches its
minimum at approximately the 15th epoch. However, the loss tends to increase
progressively thereafter. In contrast, the F1 score continues to improve
gradually even after the 15th epoch. This implies that employing validation
loss for early-stopping may hinder the model from reaching a higher F1 score,
which is the actual metric for evaluating the model performance. Additionally,
the model with early-stopping does not perform as well as the model obtained
by terminating the training at the maximal training epochs.

Based on the analysis of the control-variates approach, we can conclude that
all the aforementioned factors have a discernible impact on the final
performance of WHAR models. Therefore, their inclusion in academic papers is
crucial to ensuring the reproducibility of experiments.

Table 2: Summary of the datasets used in the experiment. The abbreviations acc, gyro, mag denote 3d accelerometers, gyroscopes and magnetometers, respectively. Name | #Subjects | #Channels | #Length | #Classes | Sensors type | Freq
---|---|---|---|---|---|---
DSADS | 8 | 45 | 126 | 19 | acc, gyro, mag | $25\,$\mathrm{Hz}$$
HAPT | 30 | 6 | 128 | 12 | acc, gyro | $50\,$\mathrm{Hz}$$
OPPO | 4 | 77 | 30 | 18 | acc, gyro, mag | $30\,$\mathrm{Hz}$$
PAMAP2 | 9 | 18 | 168 | 12 | acc, gyro | $100\,$\mathrm{Hz}$$
RWHAR | 15 | 21 | 128 | 8 | acc | $50\,$\mathrm{Hz}$$

##  5 Experiment

It has been observed that frequently used training hyperparameters derived
from reviewed articles do not yield an optimal WHAR model. Accordingly,
without using hyperparameter tuning, how should we set the parameters of the
training process to get relatively close to optimal results? To address this,
we propose a hypothesis: by employing the optimal setting for each factor
(determined during the control-variates analysis) for model training (denoted
as new), the performance of the trained model could be enhanced, surpassing
the effectiveness of the baseline used in section 4 (denoted as comm).
Specifically, our approach involves using an Adam optimizer [13] with an
initial learning rate of $1e-3$ and a weight decay of $1e-4$. In addition, a
Cosine Scheduler [16] is employed, along with the application of the cross-
entropy loss function [21]. We utilize batch training with a batch size of
$16$ and apply the F1 score on the validation set for early stopping, with a
patience of $30$ epochs. After training, the optimal model is chosen based on
the best F1 score on the validation set. In this section, we conduct an
experiment to test this hypothesis.

Benchmark WHAR datasets. To ensure experimental fairness, we conducted
experiments on five most widely used benchmark datasets, i.e., DSADS [1], HAPT
[19], OPPO [2], PAMAP2 [18], and RW [24]. As summarized in Table 2, these
datasets differ significantly in terms of sensor types, sampling rates, number
of subjects, number of channels, sequence length and application scenarios. As
data preprocessing, we applied sliding windows to split data in segments,
specifically, we employed a $50\%$ overlap between adjacent windows for the
training and validation sets. While for the test set, we used a $90\%$ overlap
between adjacent windows [11].

Model To ensure the generalizability of our new training process, three models
with different structures are utilized as our target models, namely,
Convolution Neural Network (CNN)-based model (MCNN) [14], hybrid CNN-LSTM
model (CNNLSTM) [17], and transformer-based model (Transformer) [28].

Evaluation and Metric To evaluate the performance of the final obtained models
and demonstrate their generalizability across subjects, we employ the LOSO-CV
method on all datasets. In response to the category imbalance present within
the WHAR data, we apply the F1 score as the evaluation metric. Moreover, to
ensure the robustness of our results, we repeat the experiment five times
using different random seeds and report the average results for all
experiments.

Baseline We identified the most frequently utilized training procedure in the
collected academic papers and use them as our baseline (comm). Concretely, we
use an Adam optimizer [13] with an initial learning rate of $1e-3$ without
weight decay. We use the cross-entropy loss to guide the batch training with a
batch size of $256$. We employ an LRscheduler that reduces the learning rate
by a factor of $0.1$ based on the validation loss with patience of $10$
epochs. We apply early-stopping with the patience of $30$ epochs also on
validation loss. Finally, we consider the model with the lowest validation
loss as the optimal model.

###  5.1 Result

Table 3 presents the results of our experiments. We can observe that, the new
training procedure achieved significantly better results compared to the
baseline procedure on all datasets and across all models. This enhancement
confirms the effectiveness of the proposed training procedure. In addition, it
is noteworthy to mention that, this enhancement can be gained without any
supplementary demands on the training resource and any increasing model
inference time.

Table 3: LOSO-CV performance (mean F1 score) comparison. Model | Method | DSADS | HAPT | OPPO | PAMAP2 | RW
---|---|---|---|---|---|---
MCNN | comm | 0.801 | 0.779 | 0.405 | 0.708 | 0.691
new | 0.865 | 0.802 | 0.432 | 0.734 | 0.747
CNNLSTM | comm | 0.854 | 0.806 | 0.392 | 0.735 | 0.706
new | 0.900 | 0.820 | 0.395 | 0.764 | 0.768
Transformer | comm | 0.812 | 0.767 | 0.402 | 0.654 | 0.598
new | 0.872 | 0.805 | 0.440 | 0.758 | 0.731

##  6 Conclusion and future work

In this study, we highlight the prevalent trend that, the majority of academic
papers are deficient in providing a comprehensive description of the model
training process. Employing the control-variables analysis, we affirm that,
these overlooked factors exert a significant influence on the model
performance. Therefore, the lack of these descriptions can markedly affect the
reproducibility of the achievements reported in those academic papers. In
addition, based on the control-variates analysis, we propose a new training
procedure and test its effectiveness by conducting extensive experiments on
five widely used benchmark datasets using three models with different
architectures. The experiments indicate that, the new training procedure can
achieve significantly better results compared to the most common training
procedure on all datasets and all models.

## References

  * [1] Barshan, B., Altun, K.: Daily and Sports Activities. UCI Machine Learning Repository (2013), DOI: https://doi.org/10.24432/C5C59F
  * [2] Chavarriaga, R., Sagha, H., Calatroni, A., Digumarti, S.T., Tröster, G., Millán, J.d.R., Roggen, D.: The Opportunity Challenge: A Benchmark Database for On-body Sensor-Based Activity Recognition. Pattern Recognition Letters 34(15), 2033–2042 (2013)
  * [3] Du, Y., Lim, Y., Tan, Y.: A novel human activity recognition and prediction in smart home based on interaction. Sensors 19(20), 4474 (2019)
  * [4] Duchi, J., Hazan, E., Singer, Y.: Adaptive Subgradient Methods for Online Learning and Stochastic Optimization. Journal of machine learning research 12(7) (2011)
  * [5] Günther, L.C., Kärcher, S., Bauernhansl, T.: Activity recognition in manual manufacturing: Detecting screwing processes from sensor data. Procedia CIRP 81, 1177–1182 (2019)
  * [6] Hinton, G.E., Salakhutdinov, R.R.: Reducing the Dimensionality of Data with Neural Networks. science 313(5786), 504–507 (2006)
  * [7] Huang, Y., Schaal, N., Hefenbrock, M., Zhou, Y., Riedel, T., Beigl, M.: Mcxai: Local model-agnostic explanation as two games. In: 2023 International Joint Conference on Neural Networks (IJCNN). pp. 01–08. IEEE (2023)
  * [8] Huang, Y., Zhou, Y., Hefenbrock, M., Riedel, T., Fang, L., Beigl, M.: Automatic feature engineering through monte carlo tree search. In: Joint European Conference on Machine Learning and Knowledge Discovery in Databases. pp. 581–598. Springer (2022)
  * [9] Huang, Y., Zhou, Y., Hefenbrock, M., Riedel, T., Fang, L., Beigl, M.: Universal distributional decision-based black-box adversarial attack with reinforcement learning. In: International Conference on Neural Information Processing. pp. 206–215. Springer (2022)
  * [10] Huang, Y., Zhou, Y., Riedel, T., Fang, L., Beigl, M.: randomhar: Improving ensemble deep learners for human activity recognition with sensor selection and reinforcement learning. arXiv preprint arXiv:2307.07770 (2023)
  * [11] Jordao, A., Nazare Jr, A.C., Sena, J., Schwartz, W.R.: Human Activity Recognition Based on Wearable Sensor Data: A Standardization of the State-of-the-art. arXiv preprint arXiv:1806.05226 (2018)
  * [12] Keskar, N.S., Mudigere, D., Nocedal, J., Smelyanskiy, M., Tang, P.T.P.: On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima. arXiv preprint arXiv:1609.04836 (2016)
  * [13] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv preprint arXiv:1412.6980 (2014)
  * [14] Krizhevsky, A., Sutskever, I., Hinton, G.E.: Imagenet Classification with Deep Convolutional Neural Networks. Communications of the ACM 60(6), 84–90 (2017)
  * [15] LeCun, Y., Bottou, L., Bengio, Y., Haffner, P.: Gradient-Based Learning Applied to Document Recognition. Proceedings of the IEEE 86(11), 2278–2324 (1998)
  * [16] Loshchilov, I., Hutter, F.: SGDR: Stochastic Gradient Descent with Warm Restarts. arXiv preprint arXiv:1608.03983 (2016)
  * [17] Mutegeki, R., Han, D.S.: A CNN-LSTM Approach to Human Activity Recognition. In: 2020 international conference on artificial intelligence in information and communication (ICAIIC). pp. 362–366. IEEE (2020)
  * [18] Reiss, A., Stricker, D.: Introducing A New Benchmarked Dataset for Activity Monitoring. In: 2012 16th international symposium on wearable computers. pp. 108–109. IEEE (2012)
  * [19] Reyes-Ortiz, J.L., Oneto, L., Samà, A., Parra, X., Anguita, D.: Transition-Aware Human Activity Recognition Using Smartphones. Neurocomputing 171, 754–767 (2016)
  * [20] Robbins, H., Monro, S.: A Stochastic Approximation Method. The annals of mathematical statistics pp. 400–407 (1951)
  * [21] Shannon, C.E.: A mathematical theory of communication. ACM SIGMOBILE mobile computing and communications review 5(1), 3–55 (2001)
  * [22] Simonyan, K., Zisserman, A.: Very deep convolutional networks for large-scale image recognition. arXiv preprint arXiv:1409.1556 (2014)
  * [23] Straczkiewicz, M., James, P., Onnela, J.P.: A systematic review of smartphone-based human activity recognition methods for health research. NPJ Digital Medicine 4(1), 148 (2021)
  * [24] Sztyler, T., Stuckenschmidt, H.: On-body Localization of Wearable Devices: An Investigation of Position-Aware Activity Recognition. In: 2016 IEEE International Conference on Pervasive Computing and Communications (PerCom). pp. 1–9. IEEE (2016)
  * [25] Tang, Y., Zhang, L., Min, F., He, J.: Multiscale deep feature learning for human activity recognition using wearable sensors. IEEE Transactions on Industrial Electronics 70(2), 2106–2116 (2022)
  * [26] Wu, J., Chen, X.Y., Zhang, H., Xiong, L.D., Lei, H., Deng, S.H.: Hyperparameter optimization for machine learning models based on bayesian optimization. Journal of Electronic Science and Technology 17(1), 26–40 (2019)
  * [27] Zeiler, M.D.: Adadelta: an adaptive learning rate method. arXiv preprint arXiv:1212.5701 (2012)
  * [28] Zhang, Z., Wang, W., An, A., Qin, Y., Yang, F.: A Human Activity Recognition Method Using Wearable Sensors Based on Convtransformer Model. Evolving Systems pp. 1–17 (2023)
  * [29] Zhao, H., Scholz, A., Beigl, M., Ni, S., Singaraju, S.A., Aghassi-Hagmann, J.: Printed Electrodermal Activity Sensor with Optimized Filter for Stress Detection. In: Proceedings of the 2022 ACM International Symposium on Wearable Computers. pp. 112–114 (2022)
  * [30] Zhao, H., Zhou, Y., Riedel, T., Hefenbrock, M., Beigl, M.: Improving human activity recognition models by learnable sparse wavelet layer. In: Proceedings of the 2022 ACM International Symposium on Wearable Computers. pp. 84–88 (2022)

  *[WHAR]: Wearable Human Activity Recognition
  *[LOSO]: Leave-One-Subject-Out
  *[CV]: Cross-Validation
  *[HAR]: Human Activity Recognition
  *[CNN]: Convolution Neural Network


.Article .

2019 May 62 5 959506 Zhang, et al. https://doi.org/10.1007/s11433-019-9383-y
000000

<EMAIL_ADDRESS>
<EMAIL_ADDRESS><EMAIL_ADDRESS>
# Status and perspectives of the CRAFTS extra-galactic HI survey

Kai Zhang  Jingwen Wu  Di Li  Marko Krčo  Lister Staveley-Smith  Ningyu Tang
Lei Qian  Mengting Liu  Chengjin Jin  Youling Yue  Yan Zhu  Hongfei Liu
Dongjun Yu
Jinghai Sun  Gaofeng Pan  Hui Li  Hengqian Gan  Rui Yao  FAST Collaboration
National Astronomical Observatories, Chinese Academy of Sicences, Datun Road,
Chaoyang District, Beijing 10010, People’s Republic of China;  University of
Chinese Academy of Sciences, Beijing 100049, People’s Republic of China;  CAS
Key Laboratory of FAST, NAOC, Chinese Academy of Sciences, Beijing 200101,
People’s Republic of China;  ICRAR, The University of Western Australia, 35
Stirling Highway, Crawley, WA 6009, Australia;  ARC Centre of Excellence for
All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia

###### Abstract

The Five-hundred-meter Aperture Spherical radio Telescope(FAST) is expected to
complete its commissioning in 2019. FAST will soon begin the Commensal Radio
Astronomy FasT Survey(CRAFTS), a novel and unprecedented commensal drift scan
survey of the entire sky visible from FAST. The goal of CRAFTS is to cover
more than 20000 $deg^{2}$ and reach redshift up to about 0.35. We provide
empirical measurements of the beam size and sensitivity of FAST across the
1.05 to 1.45 GHz frequency range of the FAST L-band Array of 19-beams(FLAN).
Using a simulated HI-galaxy catalogue based on the HI Mass Function(HIMF), we
estimate the number of galaxies that CRAFTS may detect. At redshifts below
0.35, over $6\,\times\,10^{5}$ HI galaxies may be detected. Below the redshift
of 0.07, the CRAFTS HIMF will be complete above a mass threshold of
$10^{9.5}\,M_{\odot}$. FAST will be able to investigate the environmental and
redshift dependence of the HIMF to an unprecedented depth, shedding light onto
the missing baryon and missing satellite problems.

Received January 28, 2019; accepted March 4, 2019; published online March 29,
2019.

HI regions and 21-cm lines, Radio telescopes and instrumentation , Statistical
and correlative studies of properties

47.55.nb, 47.20.Ky, 47.11.Fg

##  1 Introduction

HI, or neutral hydrogen is the most abundant species in the universe.
Observations of the HI 21cm line can reveal a variety of information on
galaxies, including their redshift, HI mass, central velocity, dynamical mass,
and so on [1]. Wide-field blind extragalactic HI sky surveys can be
implemented owing to the advent of multi-beam receivers which greatly improve
the efficiency and allow the surveys to cover cosmologically significant
volumes. From the HIPASS(HI Parkes All Sky Survey [2] [3]), to the recently
completed ALFALFA (Arecibo Legacy Fast ALFA [4] [5] [6] [7]) survey, blind
surveys have played a key role in exploring the HI distribution and properties
of nearby galaxies.

The HI mass function (HIMF) depicts the cosmic number density per bin of HI
mass [8] and is found to be well fitted by the Schechter function [9]. Faint-
end slopes of the HIMF are closely related to the "missing satellite problem"
[10] [11]. At high redshift (z>1.5) the total mass density of HI, or
$\Omega_{\rm HI}$, can be deduced from the absorption lines of quasar optical
spectra through damped-Lyalpha objects [12] [13], while at lower redshifts
$\Omega_{\rm HI}$ can be evaluated by the HIMF [14] [15] [16]. The HIMF is
very important in understanding the galactic HI evolution as a function of
redshift, and serves as a test of theoretical cosmological simulations [17]
[18]. With large sampled populations and spatial volumes blind HI surveys are
ideal for measuring the HIMF and for studying the environmental dependence of
the HIMF [14] [19] [20] [16]. FAST and ASKAP (The Australian Square Kilometre
Array Pathfinder) will carry out the next generation of HI blind sky surveys
[21] [22], to enable the study of the evolution of the HIMF and $\Omega_{\rm
HI}$ up to higher redshifts.

As the largest filled-aperture single-dish telescope in the world, FAST [23]
[24] is expected to finish its commissioning in 2019 [25] [26]. The Commensal
Radio Astronomy FasT Survey (CRAFTS) [25] will simultaneously conduct an
extra-galactic HI, Galactic HI imaging, pulsar search, and Fast Radio Burst
(FRB) search surveys. The predictions [21] show FAST would be an excellent
instrument for large-scale HI surveys. Based on test observations taken during
FAST commissioning, we use updated parameters of FAST and the latest HIMF from
ALFALFA survey to predict the capability of CRAFTS to detect HI galaxies.

We briefly introduce the CRAFTS survey plan in 2, and summarize several key
parameters of FAST in 3. The sensitivity of CRAFTS with regards to the
extragalactic HI survey is discussed in 4. The number of HI galaxies CRAFTS
may detect is discussed in 5. We will discuss the impact of confusion on
CRAFTS in 6, and a summary is provided in 7. The cosmological distances
calculation and cosmological corrections in this paper refer to [28] and [29],
and we assume $\rm H_{0}(Hubble\,Constant)=73\,\rm km\,\rm s^{-1}\,\rm
Mpc^{-1}$, $\rm\Omega_{m}(Density\,parameter\,of\,matter)=0.25$ and
$\rm\Omega_{\Lambda}(Density\,parameter\,of\,dark\,energy)=0.75$.

##  2 The CRAFT Survey Plan

When inactive, FAST’s surface is a partial sphere composed of over 4400 panels
connected to over 2250 actuators with an aperture of 500m. While observing,
the actuators behind the reflector deform the illuminated surface into a
300m-aperture paraboloid, with an rms(root mean square) uncertainty of
$\sim$4mm which is sufficient for observations at frequencies up to 5GHz[23].
In the case of FAST, the most efficient way to conduct a large commensal
survey is to use drift scans which have the added benefit of minimizing gain
fluctuations due to variations in the surface and feed position. CRAFTS will
observe galactic HI, extra-galactic HI, pulsars, and FRBs simultaneously while
drifting. CRAFTS will conduct two full passes surveys similarly to ALFALFA
[4], which should help alleviate the influence of Radio Frequency Interference
(RFI) and make low SNR (Signal-to-Noise Ratio) detections more reliable. It
will take CRAFTS approximately 220 full days of observation to complete each
pass [25].

While drifting, the 19-beam receiver (the FAST L-band Array of 19-beam, or
FLAN), will be rotated by $23.4\degree$ to achieve a super-Nyquist sampling.
The spacing of each scan would be $21.9^{\prime}$ in declination to fill the
gap of two outer beams so that the survey would be nearly uniformly covered as
described in [25]. Figure 1 shows a sketch of two adjacent drift scans of FLAN
using this orientation.

Figure 1: An example sketch of two adjacent drift scans of FLAN using the
orientation used by CRAFTS. Blue and red circles with a diameter of 2.9 arcmin
represent the position and the size of beams in two drift scans. The dotted
lines show the drifting tracks of individual beams.

##  3 Key FAST Parameters

FAST is located at a latitude of $25.6529\degree\rm N$. The effective
illuminated aperture size is about 300 m up to a zenith angle of
$26.4\degree$, and can be partially illuminated up to FAST’s maximum zenith
angle of $40\degree$. Thus the total sky visible from FAST is approximately
$20000\ \rm deg^{2}$ within a declination range between $-14\degree$ and
$66\degree$.

The FLAN bandwidth (1.05 GHz to 1.45 GHz) corresponds to a maximum redshift of
0.35 for the 21 cm HI line. The channel width of FLAN for the extragalactic HI
survey is about 7.6 kHz, corresponding to a velocity resolution of 1.6 km/s
for HI.

We use FAST commissioning data to estimate its beamsize, gain and system
temperature. Much of the data are taken from [26] and the parameters are all
obtained from center beam of the FLAN.

Figure 2: Panel (a): beamsize versus frequency when zenith angle is below
$26.4\degree$, the red dashed line represents the fitted result from equation
(1). Panel (b): the blue asterisks represent the fitted result of m1 by
equation (1) at different zenith angles, which tells the beamsize at the
frequency of 1250 MHz, while the red dashed line represents the fitted line
from equation (2). Panel (c): the gain versus zenith angle, the red dashed
line represents the fitted result from equation (3). Panel (d):system
temperature versus zenith angle,the red dashed line represents the fitted
result from equation (4). The parameters here are all obtained from center
beam of the 19-beam receiver(FLAN).

Due to the wide bandwidth of FLAN and the limited feed cross-section size, the
electric field of the aperture antenna tends to be uniformly distributed at
low frequencies. While at high frequencies the distribution function of
electric field that illuminates the aperture resembles a Gaussian function.
Therefore the FLAN beam size cannot be simply estimated by assuming it is
inversely proportional to frequency; at low frequencies the beamsize is
smaller than otherwise predicted. The FLAN FWHM beamsize of center beam can be
accurately estimated by

$\displaystyle\left(\dfrac{\theta}{\rm{}^{\prime}}\right)=\rm\left[\frac{m1(ZA)}{{}^{\prime}}\right]\left(\dfrac{{\rm
d}Freq/1250}{\rm
MHz}\right)^{-1}+\rm\left(\frac{m2}{{}^{\prime}}\right)\left[\left(\dfrac{\rm
Freq}{\rm MHz}\right)-1250\right],$ (1)

where $\theta$ is beamsize in arcmin, Freq is frequency in MHz, m1 is beamsize
at the frequency of 1250 MHz in arcmin and m2 is the correction factor in
arcmin. From observations, m1 is approximately 3.24 arcmin and m2 is
approximately 5.475$\times 10^{-4}$ arcmin when zenith angle is below
$26.4\degree$. Panel (a) in Fig. 2 shows how beamsize varies with frequency
when zenith angle is below $26.4\degree$.

For zenith angles above $26.4\degree$ the aperture is only partially
illuminated and thus the beamsize will increase. When zenith angle increases,
the illuminated aperture size will decrease, we assume that the illuminated
aperture size decreases linearly when zenith angle increases and thus m1 is
proportional to zenith angle. For m2 we assume it doesn’t change. Panel(b) in
Fig. 2 shows the relation between m1 and zenith angle. Thus when zenith angle
is above $26.4\degree$, m1 can be approximated by

$\displaystyle{\rm\left(\frac{m1}{{}^{\prime}}\right)}=3.24+5.41\times
10^{-2}\left[\left(\dfrac{\rm ZA}{\,\degree}\right)-26.4\right],$ (2)

where ZA is zenith angle in degree.

The gain is about 16.46 K/Jy for the center beam when zenith angle is below
$26.4\degree$ and is largely independent of frequency over the bandwidth
covered by FLAN. Gain decreases for zenith angles greater than $26.4\degree$
due to the surface being only partially illuminated as shown in Panel (c) in
Fig. 2. When zenith angle is above $26.4\degree$, the gain may be estimated by
a second degree polynomial such as

$\displaystyle\left(\frac{\rm G}{\rm
K/Jy}\right)=16.46-0.02\left[\left(\frac{\rm
ZA}{\,\degree}\right)-26.4\right]^{2}-0.12\left[\left(\frac{\rm
ZA}{\,\degree}\right)-26.4\right],$ (3)

where G is the gain in K/Jy and ZA is zenith angle in degree. At a zenith
angle of $40\degree$, the gain will decrease to about 11.0 K/Jy, with a loss
of approximately $33\%$.

Panel (d) in Fig. 2 shows the relation between system temperature and zenith
angle. We use a second-order polynomial function to estimate the relation
between system temperature and zenith angle with

$\displaystyle\left(\frac{T_{\rm sys}}{\rm K}\right)=4.9\times
10^{-3}\left(\frac{\rm ZA}{\,\degree}\right)^{2}+5.5\times
10^{-3}\left(\frac{\rm ZA}{\,\degree}\right)+17.85,$ (4)

where $T_{\rm sys}$ is system temperature in K, and ZA is zenith angle in
degree. At zenith angles above $26.4\degree$ the feed is tilted back slightly
so as to avoid spill over. However, radiation from the surrounding mountain
peaks enters the nearer sidelobes and increases the system temperature. A
ground screen made from wire mesh was proposed to reduce $\rm T_{sys}$ for
FAST when the zenith angle is large, which is designated as the
$\textquoteleft$backward illumination’ mode [27].

Fig. 3 shows an example spectrum of AGC11820 taken by FAST on 2018/10/22.

Figure 3: A spectrum of AGC11820 taken by FAST on 2018/10/22. The horizontal
axis represents radial velocity and the vertical axis represents antenna
temperature.

##  4 Sensitivity Calculation

###  4.1 Effective Integration Time

The effective integration time of a drift scan survey reflects the equivalent
rms noise by combining data from multiple observations, which may be estimated
by

$\displaystyle t_{\rm obs}/t_{\rm eff}=\Omega_{\rm obs}/\Omega_{\rm b},$ (5)

where $t_{\rm eff}$ is the effective integration time for each point in the
sky within the observed region, $t_{\rm obs}$ is the total observation time,
$\Omega_{\rm obs}$ is the total solid angle of observation, and $\Omega_{\rm
b}$ is the solid angle of the beam.

Figure 4: The upper figure shows $t_{\rm eff}$ versus DEC at redshift of 0
after one pass. The bottom figure shows $t_{\rm eff}$ after one pass as a
function of z at DEC of $25.6\degree$ and $65.6\degree$ in blue and red solid
line respectively.

We assume all 19 beams of FLAN have same beam pattern, which can be estimated
as an axisymmetric Gaussian function, so $\Omega_{\rm b}=19\times
1.13\times\theta^{2}$, where $\theta$ is the beamsize. If we assume the
drifting speed at certain declination is constant and at the equator the
drifting speed reaches its maximum, which is roughly 0.25 arcmin/s, thus the
drifting speed of survey $v_{\rm s}/\rm arcmin\ \rm s^{-1}=0.25*cos(DEC)$,
where DEC is the declination of the center beam of FLAN while drifting.
$\Omega_{\rm obs}$ can be represented by $\delta v_{\rm s}t_{\rm obs}$, where
$\delta=21.9^{\prime}$ is the spacing in declination between two adjacent
drift scans. Thus $t_{\rm eff}$ can be estimated by

$\displaystyle\left(\frac{t_{\rm eff}}{s}\right)=\frac{19\times
1.13\times\left(\frac{\theta}{{}^{\prime}}\right)^{2}}{\left(\frac{0.25}{{}^{\prime}/s}\right)\times{\rm
cos}{\left(\frac{\rm
DEC}{\degree}\right)}\left(\frac{\delta}{{}^{\prime}}\right)}.$ (6)

If we overlook the peculiar motion of the earth and HI source, the frequency
of HI line we observed is: $\nu_{\rm obs}=\nu_{\rm HI}/(1+{\rm z})$, where
$\nu_{\rm HI}=1420.4\rm MHz$ is the rest-frame HI frequency, and $\rm z$ is
the redshift of the source. The upper plot in Fig. 4 shows the effective
integration time after one pass as a function of DEC at redshift of 0. The
main factors that influence $t_{\rm eff}$ are the beamsize and $1/{\rm
cos}({\rm DEC})$. When DEC ranges between $-1.2\degree$ and $52\degree$,
$\theta$ doesn’t vary with DEC, so $t_{\rm eff}$ will change with $1/{\rm
cos}({\rm DEC})$. When DEC is below $-1.2\degree$ or above $52\degree$, the
beamsize would increase linearly with ZA, so the growth rate of $t_{\rm eff}$
will become higher at higher zenith angle. The bottom plot of Fig. 4 shows how
$t_{\rm eff}$ varies with z at two typical DECs after one pass.

Figure 5: The effective integration time map of one-pass of CRAFTS in z-DEC
plane. The pixel size is $21.9^{\prime}$ in declination and 0.005 in redshift.

Fig. 5 shows the effective integration time map of one-pass of CRAFTS in z-DEC
plane based on equation (6). The map shows that in most CRAFTS regions,
$t_{\rm eff}$ is from 35s to 60s, while at high zenith angle, $t_{\rm eff}$
will increase rapidly, especially at high declination regions, where the
drifting speed is slower thus the duration time of source in beam will
increase. CRAFTS plans to carry out a two-pass survey, so the ultimate
effective integration time is twice the value in Fig. 5.

Figure 6: The upper figure shows $S_{\rm rms}$ as a function of DEC at
redshift of 0 after one pass. Bottom figure shows $S_{\rm rms}$ after one pass
versus z at DEC of $25.6\degree$, $65.6\degree$, $-10\degree$ in blue, red and
black soild line respectively.

###  4.2 Sensitivity per Channel

The rms noise per channel or $S_{\rm rms}$, can be estimated by [6]

$\displaystyle S_{\rm rms}=\frac{T_{\rm sys}}{\rm G}\frac{1}{\sqrt{2f_{\rm
t}\Delta f_{\rm ch}t_{\rm s}}},$ (7)

where $\rm T_{sys}$ is system temperature in K, $\rm G$ is gain of the
telescope in $\rm K/Jy$, $\Delta f_{\rm ch}$ is single channel width in Hz and
$t_{\rm s}$ is integration time in s, here we can use the effective
integration time we calculated before. The factor $f_{\rm t}$ accounts for
observation details like bandpass subtraction method, spectral smoothing and
so on. For ALFALFA, $f_{\rm t}\approx 0.7$, here we adopt this value for
CRAFTS extragalactic HI survey.

The top figure in Fig. 6 shows $S_{\rm rms}$ as a function of DEC at redshift
of 0. The main factor that influences $S_{\rm rms}$ at ZA below $25.6\degree$
is the effective integration time: $S_{\rm rms}$ will decrease along the
increase of DEC. However, at high ZA, the increase of gain and $T_{\rm sys}$
will cause $S_{\rm rms}$ increase at a relatively higher rate. The bottom
figure in Fig. 6 shows $S_{\rm rms}$ varies as a function of z at three
typical DECs.

$S_{\rm rms}$ of one-pass of CRAFTS in z-DEC plane is shown in Fig. 7. Fig. 7
implies that $S_{\rm rms}$ will not fluctuate rapidly with DEC when DEC is
above $0\degree$. At higher redshift, the difference of $S_{\rm rms}$ between
two adjacent drift scans will become larger. At DEC below $10\degree$, $S_{\rm
rms}$ will increase rapidly when DEC decreases, which is caused by relatively
low $t_{\rm eff}$, high $T_{\rm sys}$ and low gain. For two-pass of CRAFTS,
$S_{\rm rms}$ can be obtained by dividing the value in Fig. 7 by square root
of 2.

Figure 7: The rms noise per channel map for CRAFTS drifting one-pass in z-DEC
plane, with same pixel size as Fig. 5.

###  4.3 Flux Limit for HI Detection

The velocity line width of HI signal at source rest frame or $\Delta V_{\rm
rest}$, can be estimated by [29]

$\displaystyle\Delta V_{\rm rest}\simeq\frac{c(1+{\rm z})}{\nu_{\rm
HI}}\Delta\nu_{\rm obs},$ (8)

where $\Delta\nu_{\rm obs}$ is the frequency line width of signal we observe,
c is the speed of light and z is the redshift of the source. Here we assume
the peculiar motion speed and line width of the source are much less than c.
The relation between line width in source’s rest frame, $\Delta V_{\rm rest}$,
and in the observed frame, $\Delta V_{\rm obs}$, can be donated by $\Delta
V_{\rm rest}=\Delta V_{\rm obs}/\left(1+{\rm z}\right)$. Thus the
corresponding observed velocity width in a single channel with channel width
of $\Delta f_{\rm ch}$ while observing an HI source at redshift of z, can be
estimated by

$\displaystyle\Delta V_{\rm ch}\simeq\frac{c(1+{\rm z})^{2}}{\nu_{\rm
HI}}{\Delta f_{\rm ch}}.$ (9)

The SNR of a signal can be estimated by [7]

$\displaystyle SNR=\left(\frac{S^{V_{\rm obs}}}{{\rm Jy}\,{\rm
km}\,{s^{-1}}}\right)\left(\frac{\Delta V_{\rm obs}}{{\rm km}\,{\rm
s^{-1}}}\right)^{-1}{f^{1/2}_{\rm smo}}\left(\frac{S_{\rm rms}}{\rm
Jy}\right)^{-1},$ (10)

where $S^{V_{\rm obs}}$ is the integrated flux density of HI line in observed
frame, we can make an assumption that HI line profile is a top-hat function,
so $S^{V_{\rm obs}}=S_{\rm peak}\Delta V_{\rm obs}$, where $S_{\rm peak}$ is
peak flux of HI line and $\Delta V_{\rm obs}$ is the line width of HI line in
observed frame. Usually $\Delta V_{\rm obs}$ can be described by $W_{50}$,
which is measured at $50\%$ level of each of two peaks. $f_{\rm smo}$ is the
number of independent channels that signals can be smoothed over. For very
broad HI signal profiles, the flux at two horns is much larger than that at
center part of profiles, so direct smoothing will give diminishing returns
[30]. We adopt the form of $f_{\rm smo}$ in [30], which used the transition of
completeness function of ALFALFA survey as the cutoff of $f_{\rm smo}$ and
smoothed the signal to full line width to calculate SNR. $f_{\rm smo}$ is
adopted as $\Delta V_{\rm obs}/\Delta V_{\rm ch}$ while $\Delta V_{\rm
obs}<10^{\rm 2.5}\ \rm km\ \rm s^{-1}$ and $10^{2.5}/\Delta V_{\rm ch}$ while
$\Delta V_{\rm obs}\geq 10^{\rm 2.5}\ \rm km\ \rm s^{-1}$, where $\Delta
V_{\rm ch}$ is the corresponding observed HI line velocity width in a single
channel.

The flux limit of the telescope while observing HI galaxies at a given SNR can
be denoted by

$\displaystyle S_{\rm lim}=SNR*\frac{S_{\rm rms}}{f_{\rm smo}^{1/2}}.$ (11)

If the peak flux of an HI galaxy signal is above $S_{\rm lim}$, we can say the
telescope could detect that galaxy.

##  5 Estimating the HI Galaxy Count

The HIMF tells us the relation between HI mass and number density of HI galaxy
in our universe, which can be well fitted by Schechter function [9]. The HIMF
could be expressed in the form of

$\displaystyle\phi(M_{\rm HI})$ $\displaystyle=$ $\displaystyle\frac{dN_{\rm
gal}}{dV\,{dlog}_{10}(M_{\rm HI)})}\,,$ (12) $\displaystyle=$
$\displaystyle{\rm ln}(10)\,\phi_{*}\,(\frac{M_{\rm
HI}}{M_{*}})^{\alpha+1}\,e^{-(\frac{M_{\rm HI}}{M_{*}})}\,,$ (13)

where $dN_{\rm gal}$ is the average number of galaxies in comoving volume
element $dV$, $\phi_{*}$ is the normalization constant, $M_{*}$ is the ‘knee
mass’ and $(\alpha+1)$ is the low-mass slope, which is usually referred as the
‘faint end’ of HIMF.

The HI mass of a galaxy, $M_{\rm HI}$, at redshift of z can be expressed by
[1] [29]

$\displaystyle\frac{M_{\rm HI}}{M_{\odot}}=\frac{2.35\times 10^{5}}{(1+{\rm
z})^{2}}\left[\frac{d_{\rm L}({\rm z})}{\rm
Mpc}\right]^{2}\left(\frac{S^{V_{\rm obs}}}{{\rm Jy}\,{\rm km}\,{\rm
s^{-1}}}\right),$ (14)

where $d_{\rm L}(z)$ is the luminosity distance to the galaxy and $S^{V_{\rm
obs}}$ is the velocity integral flux in observed frame, which can be
approximated by $S_{\rm peak}W_{50}$ if we assume HI signal is a top-hat
function. We can substitute $S_{\rm peak}$ by $S_{\rm lim}$ in equation (11)
to calculate the minimum HI mass or $M_{\rm HI,lim}$ FAST will detect. If we
assume the sensitivity of ALFALFA is 2.4 mJy [16] at resolution of $10\,{\rm
km}\,\rm s^{-1}$, for detecting an HI galaxy with a line width of $200\,{\rm
km}\,\rm s^{-1}$ at redshift of 0.05, in ALFALFA survey, $M_{\rm HI,lim}$ will
be about $10^{10}M_{\odot}$; while for two-pass CRAFTS, $M_{\rm HI,lim}$ will
be about $10^{9.3}M_{\odot}$ and $10^{9.5}M_{\odot}$ at DEC of $25.6\degree$
and $-14.0\degree$, respectively.

The method we use here to make mock catalogue is similar to [30], we integrate
the HIMF ranges from 6.2 to 14 times of ${\rm log10}\,(M_{\rm HI}/M_{\odot})$
to obtain the average HI galaxy number density and use the normalized HIMF as
the probability distribution function (PDF) of $M_{\rm HI}$. We make a mock
catalogue by using the PDF we obtain, the number of galaxy in mock catalogue
is obtained by multiplying average number density with the volume of sky
region we plan to observe. CRAFTS can detect galaxies with $M_{\rm HI}$ above
$M_{\rm HI,lim}$ in mock catalogue. Following [21], we assume the observed
line width of all galaxies is $200\,{\rm km}\,\rm s^{-1}$, which is a close
approximation of average velocity width of HI galaxies.

Using this method, we derive that the total number of HI galaxies CRAFTS will
detect in one-pass and two-pass is approximately $4.0\,\times\,10^{5}$ and
$6.5\,\times\,10^{5}$, respectively. The median redshift for CRAFTS after two
passes is close to 0.07, and the HI mass limit for detecting a galaxy with
line width of $200\,{\rm km}\,\rm s^{-1}$ at that redshift is approximately
$10^{9.5}\,M_{\odot}$. CRAFTS may not be able to detect HI galaxies
efficiently at redshift above 0.2. We may need more passes or some strategies
to increase SNR to reach higher redshift for HI galaxy detection. A detailed
description and discussion of our simulations and the methodology in deriving
the total number of HI galaxies in CRAFT survey will be presented in a
separated paper (Zhang et al. in prep.).

For the determination of ‘faint end’ of HIMF, in [33], the author discussed
the potential of FAST in detecting low mass HI galaxies in local group, from
their simulation results, two-pass CRAFTS would detect 32 galaxies with HI
mass above $10^{5}M_{\odot}$ by assuming the effective integration time is
60s, future detection on low mass galaxies will be a complementary test for
current simulation models.

##  6 Confusion

Confusion is caused by source blending in the beam. Beamsize and HI mass limit
will increase at high redshift, which will grow the impact of confusion to HI
surveys. Confusion will cause biases on flux, line width and redshift
measurement of HI galaxies, which will thus influence the calculation of
survey products like correlation functions(CF), HIMF and HI line width
functions(WF) [30]. According to previous study [21] [31], confusion might be
the main factor that limits survey capability of FAST at high redshifts due to
its relatively large beam size.

Here we use the model in [31] to analyze the impact of confusion on CRAFTS.
That work created a mock stack in the sky with velocity range of $600\,\rm
km\,s^{-1}$, which is the broadest velocity width of HI galaxy. They defined a
cylinder in redshift space centered on the target being stacked, the radius of
the cylinder is the length of beam size projected on the sky. Then they
calculated the total HI mass in the volume of cylinder as an estimation of the
confused HI mass that can not be separated from the spectrum of the target,
which is referred to $\textquoteleft$confused mass’ or $M_{\rm conf}$. We
compare this confused mass to the HI mass limit CRAFTS could detect. If
$M_{\rm conf}$ is close to $M_{\rm HI,lim}$, it will be difficult for CRAFTS
to tell whether there is confusion source in the detected signal or not.

$M_{\rm conf}$ is closely related with the beamsize and the beamsize of FAST
would vary with ZA and frequency. Fig. 8 shows the comparison of $M_{\rm
conf}$ and $M_{\rm HI,lim}$ of two-pass CRAFTS at two typical DECs. It seems
that confusion will not affect CRAFTS in detecting sources too much, because
$M_{\rm conf}$ is smaller than $M_{\rm HI,lim}$ at two typical DECs. Perhaps
it is due to the limit of integration time and that the beamsize of FAST at
high redshift will be smaller than usual.

Figure 8: The comparison of $M_{\rm HI,lim}$ and $M_{\rm conf}$ of CRAFTS
after two passes at DEC of $25.6\degree$(in blue lines) and $-14\degree$(in
red lines). Solid lines represent $M_{\rm HI,lim}$ of CRAFTS, dashed lines
represent $M_{\rm conf}$ including 2-Dimensional Correlation Function measured
from $\alpha.40$ catalogue, which tells the excess probability(above random)
of two galaxies being separated by a given distance in a rather small scale
[32]. The solid-dashed lines represent the $M_{\rm conf}$ if we assume HI
galaxies are uniformly distributed. The upper and bottom figure represents two
different results by assuming $\Omega_{\rm HI}$ is constant and $\rho_{\rm
HI}\,\propto\,(1+z)^{3}$ respectively.

##  7 Discussion and Conclusion

In this paper, we quantify the science prospect of extragalactic HI detections
based on a planned large-scale survey, namely, the Commensal Radio Astronomy
FasT Survey (CRAFTS). We use FAST commissioning data to estimate parameters
including the beamsize, the gain and the system temperature. We make a mock
catalogue based on the HIMF derived from ALFALFA by assuming the HIMF doesn’t
evolve with redshift, and HI galaxies are distributed uniformly in the nearby
universe. We also study the potential impact of confusion to CRAFTS survey
using model in [31]. We summarized the expected results from CRAFTS as the
following:

  1. 1.

FAST plans to complete a blind drift scan search of HI galaxies as part of
CRAFTS, which covers DEC between $-14\degree$ and $66\degree$, nearly
$20000\,\rm deg^{2}$ of sky in two passes. The bandwidth of the receiver
(FLAN) covers 1.05 GHz to 1.45 GHz, reaching a redshift of 0.35. The channel
width is 7.6 kHz, which corresponds to a velocity resolution of approximately
1.6 $\rm km\,s^{-1}$ at HI rest frequency.

  2. 2.

The main reflector of FAST can be fully iluminated when zenith angle is below
$26.4\degree$, with a beamsize of 2.95 arcmin at the HI rest frequency. At
zenith angles above $26.4\degree$, the mean reflector is partially illuminated
and beamsize will increase linearly with zenith angle.

  3. 3.

When zenith angle is below $26.4\degree$, the gain of FAST is largely constant
over the bandwidth of FLAN, which is close to 16.5 K/Jy. When zenith angle is
above $26.4\degree$, there will be a gain loss, at a zenith angle of
$40\degree$, the gain will decrease to approximately 11.0 K/Jy, with a loss of
approximately $33\%$.

  4. 4.

System temperature of FAST will increase with zenith angle ranging from
approximately 18 K to 26 K.

  5. 5.

The rms noise per 7.6 kHz channel of two-pass CRAFTS in most sky regions will
be between 1.1 mJy and 1.5 mJy.

  6. 6.

From our predictions, CRAFTS may detect over $6\,\times\,10^{5}$ HI galaxies
at a median redshift of 0.07 due to its wide coverage and outstanding
sensitivity performance. With such huge number of samples, we can make
unprecedented progress in studying HI survey products like the HI mass
function (HIMF), the Correlation Function (CF) and the HI Velocity Width
Function (WF) and deepening our understanding of HI distribution and its
property in the universe.

  7. 7.

CRAFTS will not be confusion limited for detecting HI galaxy because of its
limited integration time and unusual smaller beam size at high redshift.

This work is supported by National Key R$\&$D Program of China grant
No.2017YFA0402600 and grant No.2016YFA0400702; the National Natural Science
Foundation of China grant No.11690024, No.11725313, No.11590783 and
No.11803051; the International Partnership Program of Chinese Academy of
Sciences grant No.114A11KYSB20160008; CAS "Light of West China" Program; the
Young Researcher Grant of National Astronomical Observatories, Chinese Academy
of Sciences. The author would like to thank helpful discussion with Michael G.
Jones.

## References

  * [1] Roberts M. S., in Sandage M., Kristan J., eds, Galaxies and the Universe. (University of Chicago Press, Chicago, 1975), p. 309
  * [2] Barnes D. G. et al., MNRAS, 322, 486 (2001).
  * [3] Meyer M. J. et al., MNRAS, 350, 1195 (2004).
  * [4] Giovanelli R. et al., AJ, 130, 2598 (2005).
  * [5] Haynes, M. P., Giovanelli, R., Martin, A. M., et al. AJ, 142, 170 (2011).
  * [6] Giovanelli, R., $\&$ Haynes, M. P. A$\&$A Rv, 24, 1 (2015).
  * [7] Haynes, M. P., Giovanelli, R., Kent, B. R. et al., ApJ, 861, 49 (2018).
  * [8] Briggs F. H., AJ, 100, 999 (1990).
  * [9] Schechter P., ApJ, 203, 297 (1976).
  * [10] Klypin, A., Kratsov. A.V., Valenzuela, O. $\&$ Prada, F., ApJ 522, 82 (1999).
  * [11] Moore, B., Ghigna, S., Governato, F. et al., ApJ 723, 1359 (1999).
  * [12] Storrie-Lombardi L. J., Wolfe A. M., ApJ, 543, 552 (2000).
  * [13] P$\rm\acute{e}$roux C., McMahon R. G., Storrie-Lombardi L. J., Irwin M. J., MNRAS, 346, 1103 (2003).
  * [14] Zwaan M. A., Meyer M. J., Staveley-Smith L., Webster R. L., MNRAS, 359, L30 (2005).
  * [15] Martin A. M., Papastergis E., Giovanelli R., Haynes M. P., Springob C. M., Stierwalt S., ApJ, 723, 1359 (2010).
  * [16] Jones, M. G., Haynes, M. P., Giovanelli, R., $\&$ Moorman, C., MNRAS, 477, 2 (2018).
  * [17] Obreschkow D., Croton D., DeLucia G., Khochfar S., Rawlings S., ApJ, 698, 1467 (2009).
  * [18] Duffy A. R., Kay S. T., Battye R. A., Booth C. M., Dalla Vecchia C., Schaye J., MNRAS, 420, 2799 (2012a).
  * [19] Moorman C. M., Vogeley M. S., Hoyle F., Pan D. C., Haynes M. P., Giovanelli R., MNRAS, 444, 3559 (2014).
  * [20] Jones M. G., Papastergis E., Haynes M. P., Giovanelli R., MNRAS, 457, 4393 (2016b).
  * [21] Duffy A. R., Battye R. A., Davies R. D., Moss A., Wilkinson P. N., MNRAS, 383, 150 (2008).
  * [22] Duffy A. R., Meyer M. J., Staveley-Smith L., Bernyk M., Croton D. J., Koribalski B. S., Gerstmann D., Westerlund S., MNRAS, 426, 3385 (2012).
  * [23] Nan R., Sci. China G, 49, 129 (2006).
  * [24] Nan R., et al., International Journal of Modern Physics D, 20, 989 (2011).
  * [25] D. Li, P. Wang, L. Qian, et al., IEEE. 19, 112 arXiv:1802.03709 (2019).
  * [26] P. Jiang et al. (FAST project), Sci. China-Phys. Mech. Astron, Commissioning progress of FAST, in press, (2019)
  * [27] C. Jin, K, Zhu and J. Fan, et al., proceeding of the ISAP, Nanjing (2013).
  * [28] Hogg, D. W., ArXiv Astrophysics e-prints, astro-ph/9905116 (1999).
  * [29] Meyer, M., Robotham, A., Obreschkow, D., et al., PASA, 34, arXiv:1705.04210 (2017).
  * [30] Jones M. G., Papastergis E., Haynes M. P., Giovanelli R., MNRAS, 449, 1856 (2015).
  * [31] Jones, M. G., Haynes, M. P., Giovanelli, R., $\&$ Papastergis, E., MNRAS, 455, 1574 (2016a).
  * [32] Papastergis E., Giovanelli R., Haynes M. P., et al., ApJ, 776, 43 (2013).
  * [33] Li J., Wang Y.-G., Kong M.-Z., Wang J., Chen X., Guo R., RAA, 18, 003 (2018).