[orcid=0000-0001-7147-0868]

[1]

Conceptualization, Methodology, Investigation, Software, Data curation,
Visualization, Writing

1]organization=Norwegian University of Science and Technology (NTNU),
addressline=Department of Marine Technology, city=Trondheim, postcode=7052,
state=Sør-trondelag, country=Norway

Conceptualization, Methodology, Investigation, Software, Data curation,
Visualization, Writing

Conceptualization, Supervision, Resources

Conceptualization, Supervision

2]organization=Norwegian University of Science and Technology (NTNU),
addressline=Department of Engineering Cybernetics, city=Trondheim,
postcode=7034, state=Sør-trondelag, country=Norway

[1]Corresponding author

# Data Processing Framework for Ship Performance Analysis

Prateek Gupta<EMAIL_ADDRESS>[  Young-Rong Kim<EMAIL_ADDRESS>Sverre Steen<EMAIL_ADDRESS>Adil Rasheed<EMAIL_ADDRESS>[

###### Abstract

The hydrodynamic performance of a sea-going ship can be analysed using the
data obtained from the ship. Such data can be gathered from different sources,
like onboard recorded in-service data, AIS data, and noon reports. Each of
these sources is known to have their inherent problems. The current work gives
a brief introduction to these data sources as well as the common problems
associated with them, along with some examples. In order to resolve most of
these problems, a streamlined semi-automatic data processing framework for
fast data processing is developed and presented here. The data processing
framework can be used to process the data obtained from any of the above three
mentioned sources. The framework incorporates processing steps like
interpolating weather hindcast (metocean) data to ship’s location in time,
deriving additional features, validating data, estimating resistance
components, data cleaning, and outlier detection. A brief description of each
of the processing steps is provided with examples from existing datasets. The
processed data can be further used to analyse the hydrodynamic performance of
a ship.

###### keywords:

Ship in-service data AIS data Noon reports Metocean hindcast data Data
processing Ship performance analysis

Ship’s hydrodynamic performance can be assessed using the data from ship-in-
service

Data can be recorded onboard the ship, obtained via AIS or as noon reports

Gathered data needs to be cleaned and processed for performance analysis

A standardized data processing framework for preparing the data is developed

Data processing framework can be easily casted for processing any similar
datasets

##  1 Introduction

The performance of a sea-going ship is important not only to keep the fuel and
operational cost in-check but also to reduce global emissions from the
shipping industry. Analyzing the performance of a ship is also of great
interest for charter parties to estimate the potential of a ship and the
profit that can be made out of it. Therefore, driven by both the economic and
social incentives, the trade of ship performance analysis and monitoring has
been booming substantially in recent times. The importance of in-service data
in this context is very well understood by most of the stake holders, clearly
reflected by the amount of investment made by them on onboard sensors, data
acquisition systems, and onshore operational performance monitoring and
control centers.

The traditional way to evaluate the performance of a ship is using the noon
report data provided by the ship’s crew. A more exact approach, but not very
feasible for commercial vessels, was suggested by Walker and Atkins (2007),
conducting in-service sea trials in calm-water conditions on a regular basis.
With the advent of sensor-based continuous monitoring systems, the current
trend is to directly or indirectly observe the evolution of the calm-water
speed-power curve over time. ISO 19030 ISO (2016) along with several
researchers (Koboević et al. (2019); Coraddu et al. (2019)) recommends
observing the horizontal shift (along the speed axis) of the calm-water speed-
power curve, termed as the speed-loss, over time to monitor the performance of
a sea-going ship using the in-service data. Alternatively, it is suggested to
observe the vertical shift of the calm-water speed-power curve, often termed
as the change in power demand (adopted by Gupta et al. (2021a) and Carchen and
Atlar (2020)). Some researchers also formulated and used some indirect
performance indicators like fuel consumption (Koboević et al. (2019)),
resistance (or fouling) coefficient (Munk (2016); Foteinos et al. (2017);
Carchen and Atlar (2020)), (generalized) admiralty coefficient (Ejdfors
(2019); Gupta et al. (2021b)), wake fraction (Carchen and Atlar (2020)), fuel
efficiency (Kim et al. (2021)), etc. In each of these cases, it is clearly
seen (and most of the time acknowledged) that the results are quite sensitive
to the quality of the data used to estimate the ship’s performance.

The ship’s performance-related data obtained from various sources usually
inherits some irregularities due to several factors like sensor inaccuracies,
vibration of the sensor mountings, electrical noise, variation of environment,
etc., as pointed out in the Guide for Smart Functions for Marine Vessels and
Offshore Units (Smart Guide) published recently by American Bureau of Shipping
(2020). The quality of data used to carry-out ship performance analysis and
the results obtained further can be significantly improved by adopting some
rational data processing techniques, as shown by Liu et al. (2020) and Kim et
al. (2020). Another important factor is the source of data as it may also be
possible to obtain such datasets using the publicly available AIS data (You et
al. (2017)). Dalheim and Steen (2020b) presented a data preparation toolkit
based on the in-service data recorded onboard 2 ships. The presented toolkit
was developed for a specific type of dataset, where the variables were
recorded asynchronously and had to be synchronized before carrying-out ship
performance analysis. The current work would rather focus on challenges faced
while processing an already synchronized dataset.

The current paper presents a review of different data sources used for ship
performance analysis and monitoring, namely, onboard recorded in-service data,
AIS data, and noon reports, along with the characteristics for each of these
data sources. Finally, a data processing framework is outlined which can be
used to prepare these datasets for ship performance analysis and monitoring.
Although the data processing framework is developed for the performance
monitoring of ships, it may easily be casted for several other purposes. With
the easy availability of data from ships, the concept of creating digital
twins for sea-going ships is becoming quite popular. Major et al. (2021)
presented the concept of digital twin for a ship and the cranes onboard it.
The digital twin established by Major et al. (2021) can be used to perform
three main offshore operations, including remote monitoring of the ship,
maneuvering in harsh weather and crane operations, from an onshore control
center. Moreover, as pointed out by Major et al. (2021), the digital twin
technology can also be adopted for several other purposes, like predictive
maintenance, ship autonomy, etc. Nevertheless, the data processing framework
presented here can also be used to process the real-time data obtained to
create digital twins for ships in an efficient manner.

The following section discusses the art of ship performance analysis and the
bare minimum characteristics of a dataset required to do such an analysis.
Section 3 presents the above mentioned sources of data used for ship
performance analysis, their characteristics, and the tools required to process
these datasets. Section 4 presents the data processing framework which can be
used to process and prepare these datasets for ship performance monitoring.
Finally, section 5 finishes the paper with concluding remarks.

##  2 Ship Performance Analysis

The performance of a ship-in-service can be assessed by observing its current
performance and, then, comparing it to a benchmarking standard. There are
several ways to establish (or obtain) a benchmarking standard, like model test
experiments, full-scale sea trials, CFD analysis, etc. It may even be possible
to establish a benchmarking standard using the in-service data recorded
onboard a newly built ship, as suggested by Coraddu et al. (2019) and Gupta et
al. (2021b). On the other hand, evaluating the current performance of a ship
requires a good amount of data processing as the raw data collected during
various voyages of a ship is susceptible to noise and errors. Moreover, the
benchmarking standard is, generally, established for only a given
environmental condition, most likely the calm-water condition. In order to
draw a comparison between the current performance and the benchmarking
standard, the current performance must be translated to the same environmental
condition, therefore, increasing the complexity of the problem.

###  2.1 Bare Minimum Variables

For translating the current performance data to the benchmarking standard’s
environmental condition and carrying-out a reliable ship performance analysis,
a list of bare minimum variables must be recorded (or observed) at a good
enough sampling rate. The bare minimum list of variables must provide the
following information about each sampling instant for the ship: (a)
Operational control, (b) Loading condition, (c) Operational environment, and
(d) Operating point. The variables containing the above information must
either be directly recorded (or observed) onboard the ship, collected from
regulatory data sources such as AIS, or may be derived using additional data
sources, like the operational environment can be easily derived using the
ship’s location and timestamp with the help of an appropriate weather hindcast
(or metocean) data repository.

The operational control information should contain the values of the
propulsion-related control parameters set by the ship’s captain on the bridge,
like shaft rpm, rudder angle, propeller pitch, etc. The shaft rpm (or
propeller pitch, in case of ships equipped with controllable pitch propellers
running at constant rpm) is by far the most important variable here as it
directly correlates with the ship’s speed-through-water. It should be noted
that even in the case of constant power or speed mode, the shaft rpm (or
propeller pitch) continues to be the primary control parameter as the set
power or speed is actually achieved by using a real-time optimizer
(incorporated in the governor) which optimizes the shaft rpm (or propeller
pitch) to get to the set power or speed. Nevertheless, in case the shaft rpm
(or propeller pitch) is not available, it may be appropriate to use the ship’s
speed-through-water as an operational control parameter, as done by several
researchers (Farag and Ölçer (2020); Laurie et al. (2021); Minoura et al.
(2021); Liang et al. (2019)), but in this case, it should be kept in mind
that, unlike the shaft rpm (or propeller pitch), the speed-through-water is a
dependant variable strongly influenced by the loading condition and the
operational environment.

The loading condition should contain the information regarding the ship’s fore
and aft draft, which can be easily recorded onboard the ship. Although the
wetted surface area and under-water hull-form are more appropriate for a
hydrodynamic analysis, these can be derived easily using the ship’s hull form,
if the fore and aft draft is known. The operational environment should at
least contain variables indicating the intensity of wind and wave loads acting
on the ship, like wind speed and direction, significant wave height, mean wave
direction, mean wave period, etc. Finally, the operating point should contain
the information regarding the speed-power operating point for the sampling
instant. Table 1 presents the list of bare minimum variables required for ship
performance analysis. The list given in the table may have to be modified
according to ship specifications, for example, the propeller pitch is only
relevant for a ship equipped with a controllable pitch propeller.

Table 1: The list of bare minimum data variables required for ship performance analysis. Category | Variables
---|---
Operational Control | Shaft rpm, Rudder angle, & Propeller pitch
Loading Condition | Fore and aft draft
Operational Environment |  | Longitudinal and transverse wind speed, Significant wave height,
---
Relative mean wave direction, & Mean wave period
Operating Point | Shaft power & Speed-through-water

###  2.2 Best Practices

It is well-known that the accuracy of various measurements is not the same. It
also depends on the source of the measurements. The measurements recorded
using onboard sensors are generally more reliable as compared to the manually
recorded noon report measurements, due to the possibility of human error in
the latter. Even in the case of onboard recorded sensor measurements, the
accuracy varies from sensor-to-sensor and case-to-case. Some sensors can be
inherently faulty, whereas others can give incorrect measurements due to
unfavorable installation and operational conditions, and even the best ones
are known to have some measurement noise. Thus, it is recommended to establish
and follow some best practices for a reliable and robust ship performance
analysis.

The onboard measurements for shaft rpm ($n$) and shaft torque ($\tau$) are
generally obtained using a torsion meter installed on the propeller shaft,
which is considered to be quite reliable. The shaft power ($P_{s}$)
measurements are also derived from the same as the shaft power is related to
the shaft rpm and torque through the following identity: $P_{s}=2\pi n\tau$.
It should be noted that no approximation is assumed in this formulation and,
therefore, it should be validated with the data, if all three variables
($n,\tau,P_{s}$) are available. On the other hand, the measurements for speed-
through-water are known to have several problems, as presented by Dalheim and
Steen (2021). Thus, it is recommended to use shaft rpm (and not speed-though-
water) as the independent variable while creating data-driven regression
models to predict the shaft power. Owing to the same reason, it may also be a
good idea to quantify the change in ship’s performance in terms of change in
power demand rather than speed-loss (or speed-gain), as recommended by ISO
19030 ISO (2016).

Further, it is also quite common to use fuel oil consumption as a key
performance indicator for ship performance analysis (Karagiannidis and
Themelis (2021)). The fuel oil consumption can be easily calculated from the
engine delivered torque and engine rpm, if the specific fuel consumption (SFC)
curve for the engine is known. Even though the SFC curve is established and
supplied by the engine manufacturer, it is only valid for a specific operating
environment, and it is known to evolve over time due to engine degradation and
maintenance. Thus, including the fuel oil consumption in ship performance
analysis increases the complexity of the problem, which requires taking engine
health into account. If the objective of ship performance analysis is also to
take into account the engine performance, then it may be beneficial to divide
the problem into two parts: (a) Evaluate the change in power demand (for
hydrodynamic performance analysis), and (b) Evaluate the change in engine SFC
(for engine performance analysis). Now, the latter can be formulated as an
independent problem with a completely new set of variables-of-interest, like
engine delivered torque, engine rpm, ambient air temperature, calorific value
of fuel, turbocharger health, etc. This would not only improve the accuracy of
ship’s hydrodynamic performance analysis but would also allow the user to
develop a more comprehensive and, probably, accurate analysis model. The
current work is focused on the hydrodynamic performance analysis.

###  2.3 Sampling Frequency

Almost all electronics-based sensors are known to have some noise in their
measurements. The simplest way adopted to subdue this noise is by taking an
average over a number of measurements (known as a ‘sample’ in statistics),
recorded over a very short period of time (milliseconds). It is also known
that the statistical mean of a ‘sample’ converges to the true mean (i.e., the
mean of the entire population), thereby eliminating the noise, as the number
of measurements in the ‘sample’ is increased, provided the observations follow
a symmetrical distribution. Nevertheless, it is observed that the high
frequency data still retains some noise, probably due to the fact that the
number of measurements in each ‘sample’ is small, i.e., the measurements are
obtained by averaging a small number of samples recorded over a very short
period of time. On the other hand, as seen in the case of noon reports and
most of the in-service datasets, time-averaging the measurements over a longer
period of time obscures the effect of moderately varying influential factors,
for example, instantaneous incident wind and waves, response motions, etc.
Thus, a very high sampling frequency data may retain high noise, and a very
low sampling frequency data, with time-averaged values, may result in
obscuring important effects from the data time-series. Furthermore, in the
third scenario, it may be possible that the data acquisition (DAQ) system
onboard the ship is simply using low sampling frequency, recording
instantaneous values instead of time-averaged ones, saving a good amount of
storage and bandwidth while transmitting it to the shore-based control
centers. These low frequency instantaneous values may result in an even more
degraded data quality as it would contain noise as well as obscure the
moderately varying effects.

The ideal sampling frequency would also depend on the objective of the
analysis and the recorded variables. For example, if the objective of the
analysis is to predict the motion response of a ship or analyse its seakeeping
characteristics, the data should be recorded at a high enough sampling
frequency such that it is able to capture such effects. Hansen et al. (2011)
analyzed the ship’s rudder movement and the resulting resistance, and
demonstrated that if the sampling interval would be large, the overall
dynamics of the rudder movement would not be captured, resulting in a
difference in resistance. One criterion for selecting the data sampling rate
is Nyquist frequency (Jerri (1977)), which is widely used in signal
processing. According to this criterion, the sampling frequency shall be more
than twice the frequency of the observed phenomenon to sufficiently capture
the information regarding the phenomenon. Therefore, if the aim is not to
record any information regarding the above mentioned moderately varying
effects (instantaneous incident wind and waves, response motions, etc.), it
may be acceptable to just obtain low frequency time-averaged values so that
such effects are subdued. But it may still be useful to obtain high frequency
data, in this case, as it can be advantageous from data cleaning point of
view. For example, the legs of time-series showing very high variance, due to
the noise or moderately varying effects, can be removed from the analysis to
increase the reliability of results.

##  3 Data Sources, Characteristics & Processing Tools

###  3.1 In-service Data

The in-service data, referred to here, is recorded onboard a ship during its
voyages. This is achieved by installing various sensors onboard the ship,
collecting the measurements from these sensors on a regular basis (at a
predefined sampling rate) using a data acquisition (DAQ) system, and fetching
the collected data to onshore control centers. The two most important features
of in-service data is the sampling rate (or, alternatively, sampling
frequency) and the list of recorded variables. Unfortunately, there is no
proper guide or standard which is followed while defining both these features
for a ship. Thus, the in-service data processing has to be adapted to each
case individually.

The in-service datasets used here are recorded over a uniform (across all
recorded variables) and evenly-spaced sampling interval, which makes it easier
to adopt and apply data processing techniques. In an otherwise case, where the
data is sampled with a non-uniform and uneven sampling interval, some more
pre-processing has to be done in order to prepare it for further analysis, as
demonstrated by Dalheim and Steen (2020b). Dalheim and Steen (2020b) presented
a detailed algorithm to deal with time vector jumps and synchronizing non-
uniformly recorded data variables. The problem of synchronization can,
alternatively, be looked at using the well-known dynamic time warping (DTW)
technique, which is generally used for aligning the measurements taken by two
sensors, measuring the same or highly correlated features. In a different
approach, Virtanen et al. (2020) demonstrated that the collected data can be
down-sampled or up-sampled (resampling) to obtain a uniform and evenly sampled
dataset.

####  3.1.1 Inherently Faulty & Incorrect Measurements

Some of the sensors onboard a ship can be inherently faulty and provide
incorrect measurements due to unfavorable installation or operational
conditions. Many of these can actually be fixed quite easily. For instance,
Wahl (2019) presented the case of faulty installation of the wind anemometer
onboard a ship, resulting in missing measurements for head-wind condition
probably due to the presence of an obstacle right in front of the sensor. Such
a fault is fairly simple to deal with, say, by fixing the installation of the
sensor, and it is even possible to fix the already recorded dataset using the
wind measurements from one of the publicly available weather hindcast
datasets. Such an instance also reflects the importance of data exploration
and validation for ship performance analysis. Unlike above, the case of draft
and speed-through-water measurement sensors is not as fortunate and easy to
resolve.

The ship’s draft is, generally, recorded using a pressure transducer installed
onboard the ship. The pressure transducer measures the hydrostatic pressure
acting on the bottom plate of the ship which is further converted into the
corresponding water level height or the draft measurement. When the ship
starts to move and the layer of water in contact with the ship develops a
relative velocity with respect to the ship, the total pressure at the ship’s
bottom reduces due to the non-zero negative hydrodynamic pressure and,
therefore, further measurements taken by the draft sensor are incorrect. This
is known as the Venturi effect. It may seem like a simple case, and one may
argue that the measurements can be fixed by just adding the water level height
equivalent to the hydrodynamic pressure, which may be calculated using the
ship’s speed-through-water. Here, it should be noted that, firstly, to
accurately calculate the hydrodynamic pressure, one would need the localized
relative velocity of the flow (and not the ship’s speed-through-water), which
is impractical to measure, and secondly, the speed-though-water measurements
are also known to have several sources of inaccuracy. Alternatively, it may be
possible to obtain the correct draft measurements from the ship’s loading
computer. The loading computer can calculate the draft and trim in real-time
based on the information such as the ship’s lightweight, cargo weight and
distribution, and ballast water loading configuration.

The state-of-the-art speed-though-water measurement device uses the Doppler
acoustic speed log principle. Here, the relative speed of water around the
hull (i.e., the speed-though-water) is measured by observing the shift in
frequency (popularly known as the Doppler shift) of the ultrasound pulses
emitted from the ship’s hull, due to its motion. The ultrasonic pulses are
reflected by the ocean bottom, impurities in the surrounding water, marine
life, and even the liquid-liquid interface between the density difference
layers in deep ocean. The speed of water surrounding the ship is influenced by
the boundary layer around the hull so it is required that the ultrasonic
pulses reflected only by the particles outside the boundary layer are used to
estimate the speed-though-water. Therefore, a minimum pulse travelling
distance has to be prescribed for the sensor. If the prescribed distance is
too larger or if the ship is sailing in shallow waters, the Doppler shift is
calculated using the reflection from the ocean bottom, i.e., the sensor is in
ground-tracking mode, and therefore, it would clearly record the ship’s speed-
over-ground instead of the speed-though-water. Dalheim and Steen (2021)
presented a detailed account regarding the uncertainty in the speed-though-
water measurements for a ship, commenting that the speed log sensors are
considered to be one of the most inaccurate ones onboard the ship.

It may also be possible to estimate the speed-though-water of a ship using the
ship’s speed-over-ground and incident longitudinal water current speed. The
speed-over-ground of a ship is measured using a GPS sensor, which is
considered to be quite accurate, but unfortunately, the water current speed is
seldom recorded onboard the ship. It is certainly possible to obtain the water
current speed from a weather hindcast data source, but the hindcast
measurements are not accurate enough to obtain a good estimate for speed-
through-water, as indicated by Antola et al. (2017). It should also be noted
that the temporal and spatial resolution of weather hindcast data is
relatively larger than the sampling interval of the data recorded onboard the
ship. Moreover, the water current speed varies along the depth of the sea,
therefore, the incident longitudinal water current speed must be calculated as
an integral of the water current speed profile over the depth of the ship.
Thus, in order to obtain accurate estimates of speed-though-water, the water
current speed has to be measured or estimated upto a certain depth of the sea
with good enough accuracy, which is not possible with the current state-of-
the-art.

####  3.1.2 Outliers

Another big challenge with data processing is the problem of detecting and
handling outliers. As suggested by Olofsson (2020), it may be possible to
categorize outliers into the following two broad categories: (a) Contextual
outliers, and (b) Correlation-defying outliers111Called collective outliers by
Olofsson (2020).. Dalheim and Steen (2020b) presented methods to detect and
remove contextual outliers, further categorized as (i) obvious (or invalid)
outliers, (ii) repeated values, (iii) drop-outs, and (iv) spikes. Contextual
outliers are easily identifiable as they either violate the known validity
limits of one or more recorded variables (as seen in the case of obvious
outliers and spikes) or present an easily identifiable but anomalous pattern
(as seen in the case of repeated values and drop-outs).

The case of correlation-defying outliers is much more difficult to handle, as
they can easily blend into the cleaned data pool. The two most popular methods
which can be used to identify correlation-defying outliers are Principal
Component Analysis (PCA) and autoencoders. Both these methods try to
reconstruct the data samples after learning the correlation between the
variables. It is quite obvious that a correlation-defying outlier would result
in an abnormally high reconstruction error and, therefore, can be detected
using such techniques. In a recent attempt, Thomas and Judith (2021)
demonstrated an ensemble method combining PCA and autoencoders coupled with
isolation forest to detect such outliers.

####  3.1.3 Time-Averaging Problem

As aforementioned, the onboard recorded in-service data can be supplied as
time-averaged values over a short period of time (generally upto around 15
minutes). Although the time-averaging method eliminates white noise and
reduces the variability in the data samples, it introduces a new problem in
case of angular measurements. The angular measurements are, generally,
recorded in the range of 0 to 360 degrees. When the measurement is around 0 or
360 degrees, it is obvious that the instantaneous measurements, reported by
the sensor, will fluctuate in the vicinity of 0 and 360 degrees. For instance,
assuming that the sensor reports a value of about 0 degree for half of the
averaging time and about 360 degrees for the remaining time, the time-averaged
value recorded by the data acquisition (DAQ) system will be around 180
degrees, which is significantly incorrect. Most of the angular measurements
recorded onboard a ship, like relative wind direction, ship heading, etc., are
known to inherit this problem, and it should be noted that, unlike the example
given here, the incorrect time-averaged angle can take any value between 0 and
360 degrees, depending on the instantaneous values over which the average is
calculated.

Although it may be possible to fix these incorrect values using a carefully
designed algorithm, there is no established method available at the moment.
Thus, it is suggested to fix these measurements using an alternate source for
the data variables. For example, the wind direction can be gathered easily
from a weather hindcast data source. Thus, it can be used to correct or just
replace the relative wind direction measurements, recorded onboard the ship.
The ship’s heading, on the other hand, can be estimated using the latitude and
longitude measurements from the GPS sensor.

###  3.2 AIS Data

AIS is an automatic tracking system that uses transceivers to help ships and
maritime authorities identify and monitor ship movements. It is generally used
as a tool for ship transportation services to prevent collisions during
navigation. Ships over 300 tons must be equipped with transponders capable of
transmitting and receiving all message types of AIS under the SOLAS
Convention. AIS data is divided into dynamic (position, course, speed, etc.)
static (ship name, dimensions, etc.), and voyage-related data (draft,
destination, ETA, etc.). Dynamic data is automatically transmitted every 2-10
seconds depending on the speed and course of the ship, and if anchored, such
information is automatically transmitted every 6 minutes. On the other hand,
static and voyage-related data is provided by the ship’s crew, and it is
transmitted every 6 minutes regardless of the ship’s movement state.

Since dynamic information is automatically updated based on sensor data, it is
susceptible to faults and errors, similar to those described in section 3.1.1.
In addition, problems may occur even in the process of collecting and
transmitting data between AIS stations, as noted by Weng et al. (2020). The
AIS signal can also be influenced by external factors, such as weather
conditions and Earth’s magnetic field, due to their interference with the very
high frequency (VHF) equipment. Therefore, some of the AIS messages are lost
or get mixed. Moreover, the receiving station has a short time slot during
which the data must be received, and due to heavy traffic in the region, it
fails to receive the data from all the ships in that time. In some cases,
small ships deliver inaccurate information due to incorrectly calibrated
transmitters, as shown by Weng et al. (2020). In a case study, Harati-Mokhtari
et al. (2007) observed that 2% of the MMSI (Maritime Mobile Service Identity)
information was incorrect and 30% of the ships were not properly marked with
the correct navigation status. In the case of ship dimensions, about 18% of
the information was found to be inaccurate. Therefore, before using AIS raw
data for ship performance analysis, it is necessary to check key parameters
such as GPS position, speed, and course, and the data identified as incorrect
must be fixed.

####  3.2.1 Irrational Speed Data

The GPS speed (or speed-over-ground) measurements from AIS data may contain
samples that have a sudden jump compared to adjacent samples or excessively
higher or lower value than the normal operating range. This type of inaccurate
data can be identified through comparison with location and speed data of
adjacent samples. The distance covered by the ship at the corresponding speed
during the time between the two adjacent AIS messages is calculated, and the
distance between the actual two coordinates is calculated using the Haversine
formula (given by equation 1) to compare the two values. If the difference
between the two values is negligible, the GPS speed can be said to be normal,
but if not, it is recommended to be replaced with the GPS speed value of the
adjacent sample. It should be noted that if the time difference between the
samples is too short, the deviation of the distance calculated through this
method may be large. In such a case, it is necessary to consider the average
trend for several samples. If there are no valid samples nearby or the GPS
coordinate data is problematic, one can refer to the normal service speed
according to the ship type, as shown in table 2, or if available, a more
specific method such as normalcy box (Rhodes et al. (2005); Tu et al. (2017)),
which defines the speed range of the ships according to the geographic
location, may be applied.

${D=2r\sin^{-1}\left(\sqrt{\sin^{2}\left(\frac{y_{i+1}-y_{i}}{2}\right)+\cos{\left(y_{i}\right)}\cos{\left(y_{i+1}\right)}\sin^{2}\left(\frac{x_{i+1}-x_{i}}{2}\right)}\right)}$
(1)

Where $D$ is the distance between two coordinates ($x_{i}$, $y_{i}$) and
($x_{i+1}$, $y_{i+1}$), $r$ is the radius of Earth, and ($x_{i}$, $y_{i}$) is
the longitude and latitude at timestamp $i$.

Table 2: Typical service speed range of different ship types, given by Solutions (2018). Category | Type | Service speed (knot)
---|---|---
Tanker | Crude oil carrier | 13-17
| Gas tanker/LNG carrier | 16-20
| Product | 13-16
| Chemical | 15-18
Bulk carrier | Ore carrier | 14-15
| Regular | 12-15
Container | Line carrier | 20-23
| Feeder | 18-21
General cargo | General cargo | 14-20
| Coaster | 13-16
Roll-on/roll-off cargo | Ro-Ro/Ro-Pax | 18-23
Passenger ship | Cruise ship | 20-23
| Ferry | 16-23

####  3.2.2 Uncertainty due to Human Error

AIS data, excluding dynamic information, is not automatically updated by the
sensors, but it is logged by the ship’s crew manually, so there is a
possibility of human error. This includes information such as the draft,
navigation status, destination, and estimated time of arrival (ETA) of the
ship. Although it is difficult to clearly distinguish the incorrectly entered
information, it is possible to indirectly determine whether the manual input
values have been updated using the automatically logged dynamic information.
Each number in navigation status represents ship activity such as ‘under way
using engine (0)’, ‘at anchorage (1)’, and ‘moored (5)’. If this field is
being updated normally, it should be ‘0’ if the ship is in-trip and ‘5’ if it
is at berth. If the navigation status of the collected AIS data is ‘1’ or ‘5’
above a certain GPS speed (or speed-over-ground), or if the state is set to
‘0’ even when the speed is 0 and the location is within the port, the AIS data
have not been updated on time and other manually entered information should
also be questioned.

###  3.3 Noon Report Data

Ships engaged in international navigation of more than 500 gross tons are
required to send a noon report to the company, which briefly records what
happened on the ship from previous noon to present noon. The noon report must
basically contain sufficient information regarding the location, course,
speed, and internal and external conditions affecting the vessel’s voyage.
Additionally, the shipping company collects information related to fuel
consumption and remaining fuel onboard, propeller slip, average RPM, etc. as
needed. Such information is often used as a ship’s management tool and
reference data, such as monitoring and evaluating ship’s performance,
calculating energy efficiency operating indicators, and obtaining fuel and
freshwater order information. Despite its customary use, the standardized
information in the noon reports may not be sufficient to accurately assess the
performance of the ship, due to several problems discussed as follows. This
information is based on the average values from noon to noon. For an accurate
ship performance analysis, higher frequency samples and additional data may be
recommended.

####  3.3.1 Uncertainties due to Averaging Measurements & Human Error

Basically, information reported through the noon reports is created based on
the measurement values of the onboard sensor. Therefore, it also has the
possibility to involve the problem of inherently faulty sensors and incorrect
measurements, as discussed in section 3.1.1. Apart from the problems caused by
sensors, the noon report data may have problems caused by the use of 24-hour
averaged values and human errors. The data collection interval is once a day
and the average of the values recorded for 24 hours is reported, thus,
significant inaccuracies may be included in the data. Aldous et al. (2015)
performed a sensitivity analysis to assess the uncertainty due to the input
data for ship performance analysis using continuously recorded in-service data
and noon reports. It was observed here that the uncertainty of the outcome was
significantly sensitive to the number of samples in the dataset. In other
words, such uncertainty can be mitigated through the use of data representing
longer time-series, data collection with higher frequency, and data
processing. These results were also confirmed by Park et al. (2017) and
Themelis et al. (2018). Park et al. (2017) demonstrated in a case study that
the power consumption between the noon reports and the recorded sensor data
differed by 6.2% and 17.8% in ballast and laden voyage, respectively.

Using the averaged values over a long time period, as in the case of noon
reports, the variations due to acceleration/deceleration and maneuvering
cannot be captured. In particular, in the case of ships that sail relatively
short voyages such as feeder ships and ferries, inappropriate data for
performance analysis may be provided due to frequent changes in the
operational state. In the case of information regarding the weather and sea
states, the information generally corresponds to the condition right before
the noon report is sent from the ship, therefore, it is not easy to account
for the changes in the performance of the ship due to the variation of weather
conditions during the last 24 hours. In general, the information to be logged
in the noon report is read and noted by a person from onboard sensors. Thus,
it is possible that the time at which the values are read from the sensors
everyday may be different as well as different sensors may be used for the
values to be logged for the same field. In addition, there may be cases when
the observed value is incorrectly entered into the noon report. Thus, if the
process of preparing the noon reports is not automated, there would always be
a possibility of human errors in the data.

##  4 Results: Data Processing Framework

The results here are presented in the form of the developed data processing
framework, which can be used to process raw data obtained from one of the
above mentioned data sources (in section 3) for ship performance analysis. The
data processing framework is designed to resolve most of the problems cited in
the above section. Figure 1 shows the flow diagram for the data processing
framework. The following sections will explain briefly the consecutive
processing steps of the given flow diagram. It may be possible that the user
may not able to carry-out each step due to unavailability of some information
or features in the dataset, for example, due to the unavailability of the GPS
data (latitude, longitude and timestamp variables), it may not be possible to
interpolate weather hindcast data. In such a case, it is recommended to skip
the corresponding step and continue with the next one.

The data processing framework has been outlined in such a manner that, after
being implemented, it can be executed in a semi-automatic manner, i.e.,
requiring limited intervention from the user. The semi-autonomous nature of
the framework would also result in fast data processing, which can be
important for very large datasets. The implementation of the framework in
terms of executable code is also quite important to obtain a semi-automatic
and fast implementation of the data processing framework. Therefore, it is
recommended to adopt best practices and optimized algorithms for each
individual processing step according to the programming language in use. On
another note, the reliability of the data processing activity is also quite
critical to obtain good results. Therefore, it is important to carry-out the
validation of work done in each processing step by creating visualization (or
plots) and inspecting them for any undesired errors. The usual practice
adopted here, while processing the data using the framework, is to create
several such visualizations, like time-series plots of data variables in trip-
wise manner (explained later in section 4.2), at the end of each processing
step and then inspecting them to validate the outcome.

Raw DataEnsure Uniform Time StepsDivide into TripsInterpolate Hindcast (Using
GPS Data)Weather HindcastDerive New FeaturesInterpolation Error?Validation
ChecksData Processing Errors Detected?Fix Draft & TrimCalculate Hydrostatics
(Displacement, WSA, etc.)Ship ParticularsCalculate Resistance ComponentsData
Cleaning & Outlier DetectionProcessed DataNoYesYesNo Figure 1: Data processing
framework flow diagram.

###  4.1 Ensure Uniform Time Steps

Ensuring uniform and evenly-spaced samples would not only make it easier to
apply time-gradient-based data processing or analysis steps but would also
help avoid any misunderstanding while visualizing the data, by clearly showing
a gap in the time-series plots (when plotted against sample numbers) and
removing any abrupt jumps in the data values. Depending on the data
acquisition (DAQ) system, the in-service data recorded onboard a ship is
generally recorded with a uniform and evenly spaced sampling interval.
Nevertheless, it is observed that the extracted sub-dataset from the main
database may contain several missing time steps (or timestamps). In such a
case, it is recommended to check for such missing timestamps by simply
calculating the gradient of timestamps, and for each missing timestamp, just
add an empty row consisting only the missing timestamp value. Finally, the
dataset should be sorted according the timestamps, resulting in a uniform and
evenly-spaced list of samples.

Similar procedure can be adopted for a noon report dataset. The noon reports
are generally recorded every 24 hours, but it may sometimes be more or less
than 24 hours if the vessel’s local time zone is adjusted, specially on the
day of arrival or departure. The same procedure may not be feasible in case of
AIS data, as the samples here are sporadically distributed in general. Here,
the samples are collected at different frequencies depending on the ship’s
moving state, surrounding environment, traffic, and the type of AIS receiving
station (land-based or satellite). It is observed here that the data is
collected in short and continuous sections of the time-series, leaving some
large gaps between samples, as shown in figure 2. Here, it is recommended to
first resample the short and continuous sections of AIS data to a uniform
sampling interval through data resampling techniques, i.e., up-sampling or
down-sampling (as demonstrated by Virtanen et al. (2020)), and then, fill the
remaining large gaps with empty rows.

Figure 2: Down-sampling the collected AIS data to 15 minutes interval.

###  4.2 Divide Into Trips

Using conventional tools, data visualization becomes a challenge if the number
of samples in the dataset is enormously large. It may simply not be practical
to plot the whole time-series in a single plot. Moreover, dividing the time-
series into individual trips may be considered as neat and help discretize the
time-series into sensible sections which may be treated individually for
further data processing and analysis. Plotting an individual trip would also
give a complete overview of a port-to-port journey of the ship. Dividing the
data into trips and at-berth legs would also make further data processing
computationally less expensive as it may be possible to ignore a large number
of samples (for further steps) where the ship is not in a trip. For such
samples, it may not be necessary to interpolate hindcast, calculate
hydrostatics, calculate resistance components, etc. Lastly, identifying
individual trips would also make draft and trim correction step easier.

Dividing data into trips is substantially easier for noon reports and AIS data
as they are generally supplied with a source and/or destination port name. In
case of in-service data, it may be possible that no such information is
available. In such a case, if the GPS data (latitude and longitudes) is
available, it may be possible to just plot the samples on the world map and
obtain individual trips by looking at the port calls. Alternatively, if the
in-service data is supplied with a ‘State’ variable222Generally available for
ships equipped with Marorka systems (www.marorka.com). (mentioned by Gupta et
al. (2019)), indicating the propulsive state of the ship, like ‘Sea Passage’,
‘At Berth’, ‘Maneuvering’, etc., it is recommended to find the continuous legs
of ‘At Berth’ state and enumerate the gaps in these legs with trip numbers,
containing the rest of the states, as shown in figure 3(a). Otherwise, it is
recommended to use the shaft rpm and GPS speed (or speed-over-ground) time-
series to identify the starting and end of each port-to-port trip. Here, a
threshold value can be adopted for the shaft rpm and GPS speed. All the
samples above these threshold values (either or both) are considered to be in-
trip samples, as shown in figure 3(b). Thus, continuous legs of such in-trip
samples can simply be identified and enumerated. It may also be possible to
append few samples before and after each of these identified trips to obtain a
proper trip, starting from zero and ending at zero. Such a process is designed
keeping in mind the noise in the shaft rpm and GPS speed variables when the
ship is actually static. Finally, if the GPS data is available, further
adjustments can be done by looking at the port calls on the world map plotted
with the GPS data.

(a) Splitting time-series into trips using the ‘State’ variable.

(b) Splitting time-series into trips using threshold values (indicated by
dashed red lines) for shaft rpm (10 rpm) and GPS speed (3 knots) variables.

Figure 3: Splitting time-series into trips.

###  4.3 Interpolate Hindcast & GPS Position Correction

Even if the raw data contains information regarding the state of the weather
for each data sample, it may be a good idea to interpolate weather hindcast
(or metocean) data available from one of the well-established sources. The
interpolated hindcast data would not only provide a quantitative measure of
the weather conditions (and, consequently, the environmental loads)
experienced by the ship, but it would also help carry-out some important
validation checks (discussed later in section 4.5). In order to interpolate
hindcast data, the information regarding the location (latitude and longitude)
and recording timestamp must be available in the ship’s dataset. For ship
performance analysis, it should be aimed that, at least, the information
regarding the three main environmental load factors, i.e., wind, waves and sea
currents, is gathered from the weather hindcast sources. For a further
detailed analysis, it may also be a good idea to obtain additional variables,
like sea water temperature (both surface and gradient along the depth of the
ship), salinity, etc.

Before interpolating the weather hindcast data to the ship’s location and
timestamps, it is recommended to ensure that the available GPS (or navigation)
data is validated and corrected (if possible) for any errors. If the GPS data
is inaccurate, weather information at the wrong location is obtained,
resulting in incorrect values for further analysis. For instance, the ship’s
original trajectory obtained from the GPS data, presented in figure 4(a),
shows that the ship proceeds in a certain direction while suddenly jumping to
an off-route location occasionally. The ship, of course, may have gone off-
route as shown here, but referring to the GPS speed and heading of the ship at
the corresponding time, shown in figure 4(b), it is obvious that the
navigation data is incorrect. Here, such an irrational position change can be
detected through the two-stage steady-state (or stationarity) filter suggested
by Gupta et al. (2021b), based on the method developed by Dalheim and Steen
(2020a). The first stage of the filter uses a sliding window to remove
unsteady samples by performing a t-test on the slope of the data values, while
the second stage performs an additional gradient check for the samples failing
in the first stage to retain the misidentified samples. The ‘irrational
position’ in figure 4(a) shows the coordinates identified as unsteady when the
above two-stage filter is applied to longitude and latitude time-series. The
filtered trajectory is further obtained after removing the samples with
‘irrational position’ from the original data.

(a) Original trajectory and filtered trajectory with irrational GPS position.

(b) Trends of GPS speed, heading, and position of the ship according to the
corresponding period.

Figure 4: GPS position cleaning using the steady-state detection algorithm.

The hindcast data sources generally allow downloading a subset of the
variables, timestamps, and a sub-grid of latitudes and longitudes, i.e., the
geographical location. Depending on the hindcast source, the datasets can be
downloaded manually (by filling a form), using an automated API script, or
even by directly accessing their ftp servers. It may also be possible to
select the temporal and spatial resolution of the variables being downloaded.
In some cases, the hindcast web servers allows the users to send a single
query, in terms of location, timestamp, and list of variables, to extract the
required data for an individual sample. But every query received by these
servers is generally queued for processing, causing substantially long waiting
times, as they are facing a good amount of traffic from all over the world.
Thus, it is recommended to simply download the required subset of data on a
local machine for faster interpolation.

Once the hindcast data files are available offline, the main task at hand is
to understand the cryptic (but highly efficient) data packaging format. Now-a-
days, the two most poplar formats for such data files are GRIdded Binary data
(GRIB) and NetCDF. GRIB (available as GRIB1 or GRIB2) is the international
standard accepted by World Meteorological Organization (WMO), but due to some
compatibility issues with windows operating systems, it may be preferable to
use the NetCDF format.

Finally, a step-by-step interpolation has to be carried-out for each data
sample from the ship’s dataset. Algorithm 1 shows a simple procedure for n-th
order (in time) interpolation scheme. Here, the spatial and temporal
interpolation is performed in steps 10 and 12, respectively. For a simple and
reliable procedure, it is recommended to perform the spatial interpolation
using a grid of latitudes and longitudes around the ship’s location, after
fitting a linear or non-linear 2D surface over the hindcast grid. It may be
best to use a linear surface here as, firstly, the hindcast data may not be so
accurate that performing a higher order interpolation would provide any better
estimates, and secondly, in some case, higher order interpolation may result
in highly inaccurate estimates, due to the waviness of the over-fitted non-
linear surface. Similar arguments can be given in the case of temporal
interpolation, and therefore, a linear interpolation in time can also be
considered acceptable. The advantage of using the given algorithm is that the
interpolation steps, here, can be easily validated by plotting contours (for
spatial interpolation) and time-series (for temporal interpolation).

Algorithm 1 A simple algorithm for n-th order interpolation of weather
hindcast data variables.

1:$wData\leftarrow$ weather hindcast data

2:$x\leftarrow$ data variables to interpolate from hindcast

3:$wT\leftarrow$ timestamps in $wData$

4:for all timestamps in ship’s dataset do

5: $t\leftarrow$ current ship time stamp

6: $loc\leftarrow$ current ship location (latitude & longitude)

7: $i\leftarrow n+1$ indices of $wT$ around $t$

8: for all $x$ do

9: for all $i$ do

10: $x[i]\leftarrow$ 2D spatial interpolation at $loc$ using $wData[x][i,:,:]$

11: end for

12: $X\leftarrow$ n-th order temporal interpolation at $t$ using $x[i]$

13: end for

14:end for

An important feature of hindcast datasets is masking the invalid values. For
instance, the significant wave height should only be predicted by the hindcast
model for the grid nodes which fall in the sea, requesting the value of such a
variable on land should result in an invalid value. Such invalid values (or
nodes) are by default masked in the downloaded hindcast data files, probably
for an efficient storage of the data. These masked nodes may be filled with
zeros before carrying-out the spatial interpolation in step 10, as one or more
of these nodes may be contributing to the interpolation. Alternatively, if a
particular masked node is contributing to the interpolation, it can be set to
the mean of other nodes surrounding the point of interpolation, as suggested
by Ejdfors (2019). It is argued by Ejdfors (2019) that this would help avoid
the artificially low (zero) values during the interpolation, but if the grid
resolution is fine-enough, it is expected that the calculated mean (of
unmasked surrounding nodes) would also not be much higher than zero.

###  4.4 Derive New Features

Interpolating the weather hindcast variables to ship’s location at a given
time would provide the hindcast variables in the global (or the hindcast
model’s) reference frame. For further analysis, it may be appropriate to
translate these variables to ship’s frame of reference, and furthermore, it
may be desired to calculate some new variables which could be more relevant
for the analysis or could help validate the assimilated (ship and hindcast)
dataset. The wind and sea current variables, obtained from the hindcast source
and the ship’s dataset, can be resolved into the longitudinal and transverse
speed components for validation and further analysis. Unfortunately, the wave
load variables cannot be resolved in a similar manner, but the mean wave
direction should be translated into the relative mean wave direction (relative
to the ship’s heading or course).

###  4.5 Validation Checks

Although it is recommended to validate each processing step by visualizing (or
plotting) the task being done, it may be a good idea to take an intermediate
pause and perform all types of possible validation checks. These validation
checks would not only help assess the dataset from reliability point of view
but can also be used to understand the correlation between various features.
The validation checks can be done top-down, starting from the most critical
feature to the least one. As explained in section 2.2, the shaft power
measurements can be validated against the shaft rpm and shaft torque
measurements, if these are available, else just plotting the shaft rpm against
the shaft power can also provide a good insight into the quality of data. For
a better assessment, it is suggested to visualize the shaft rpm vs shaft power
overlaid with the engine operational envelope and propeller curves, as
presented by Liu et al. (2020) (in figure 11). Any sample falling outside the
shaft power overload envelope (specially at high shaft rpm) should be removed
from the analysis, as they may be having measurement errors. It may also be
possible to make corrections, if the shaft power data seems to be shifted (up
or down) with respect to the propeller curves due to sensor bias.

The quality of speed-through-water measurements can be assessed by validating
it against its estimate, obtained as a difference between the speed-over-
ground and longitudinal current speed. Here, it should be kept in mind that
the two values may not be a very good match due to several problems cited in
section 3.1.1. Visualizing the speed-though-water vs shaft power along with
all the available estimates of the speed-power calm-water curve is also an
important validation step (shown in figure 5). Here, the majority of
measurement data should accumulate around these curves. In case of disparity
between the curves, the curve obtained through the sea trial of the actual
ship may take precedence.

Figure 5: Speed-though-water (log speed) vs shaft power with various estimates
of speed-power calm-water curves.

The interpolated weather hindcast data variables must also be validated
against the measurements taken onboard the ship. This is quite critical as the
sign and direction notations assumed by the hindcast models and ship’s sensors
(or data acquisition system) are probably not the same, which may cause
mistakes during the interpolation step. Moreover, most ships are generally
equipped with anemometers that can measure the actual and relative wind speed
and directions, and these two modes (actual or relative) can be switched
through a simple manipulation by the crew onboard. It is possible that this
mode change may have occurred during the data recording duration, resulting in
errors in the recorded data. In addition, there may be a difference between
the reference height of the wind hindcast data and the vertical position of
the installed anemometer, which may lead to somewhat different results even at
the same location at sea. The wind speed at the reference height
(${V_{WT}}_{ref}$) can be corrected using the anemometer recorded wind speed
($V_{WT}$), assuming a wind speed profile, as follows (recommended by ITTC
(2017)):

${V_{WT}}_{ref}=V_{WT}\left(\frac{Z_{ref}}{Z_{a}}\right)^{\frac{1}{9}}$ (2)

Where $Z_{ref}$ is the reference height above the sea level and $Z_{a}$ is the
height of the anemometer.

Finally, these wind measurements can be translated into the longitudinal and
transverse relative components. The obtained transverse relative wind speed
can be validated against the transverse wind speed, obtained from the hindcast
source, as they are basically the same. Similarly, the difference between the
longitudinal relative wind speed and the speed-over-ground of the ship can be
validated against the longitudinal wind speed measurements from hindcast, as
shown in figure 6. In case of time-averaged in-service data, the problem of
faulty averaging of angular measurements when the measurement values are near
0 or 360 degrees (i.e., the angular limits), explained in section 3.1.3, must
also be verified and appropriate corrective measures should be taken. From
figure 6, it can be clearly seen that the time-averaging problem (in relative
wind direction) causes the longitudinal wind speed (estimated using the ship
data) to jump from positive to negative, resulting in a mismatch with the
corresponding hindcast values. In such a case, it is recommended to either fix
these faulty measurements, which may be difficult as there is no proven way to
do it, or just use the hindcast measurements for further analysis.

Figure 6: Validating longitudinal wind speed obtained using the ship data
against the values obtained from the hindcast. The time-averaging problem with
angular measurements around 0 or 360 degrees (explained in section 3.1.3) is
clearly visible here.

As discussed in the case of noon reports in section 3.3.1, weather information
generally refers to the state of the weather at the time when the report is
logged, which is probably not the average state from noon to noon.
Furthermore, the wind loads here are observed based on the Beaufort scale,
therefore, the deviation may be somewhat large when converted to the velocity
scale. In this case, it is recommended to consider the daily average values
obtained from the weather hindcast data, over the travel region, rather than
the noon report values.

###  4.6 Data Processing Errors

The validation step is very critical in finding out any processing mistakes or
inherent problems with the dataset, as demonstrated in the previous section.
Such problems or mistakes, if detected, must be corrected or amended for
before moving forward with the processing and analysis. The main mistakes
found at this step are generally either interpolation mistakes or incorrect
formulation of the newly derived feature. These mistakes should be rectified
accordingly, as shown in the flow diagram (figure 1).

###  4.7 Fix Draft & Trim

The draft measurements recorded onboard the ship are often found to be
incorrect due to the Venturi effect, explained briefly in section 3.1.1. The
Venturi effect causes the draft measurements to drop to a lower value due to a
non-zero negative dynamic pressure as soon as the ship develops a relative
velocity with respect of the water around the hull. Thus, the simplest
solution to fix these incorrect measurements is by interpolating the draft
during a voyage using the draft measured just before and after the voyage.
Such a simple solution provides good results for a simple case where the draft
of the ship basically remains unchanged during the voyage, except for the
reduction of draft due to consumed fuel, as shown in the figure 7(a).

(a) Simple draft correction.

(b) Complex draft correction.

Figure 7: Correcting in-service measured draft.

In a more complex case where the draft of the ship is changed in the middle of
the voyage and the ship is still moving, i.e., conducting ballasting
operations or trim adjustments during transit, the simple draft interpolation
would result in corrections which can be way off the actual draft of the
vessel. As shown in figure 7(b), the fore draft is seen to be dropping and the
aft draft increasing in the middle of the voyage without much change in the
vessel speed, indicating trim adjustments during transit. In this case, a more
complex correction is applied after taking into account the change in draft
during the transit. Here, first of all, a draft change operation is identified
(marked by green and red vertical lines in figure 7(b)), then the difference
between the measurements before and after the operation is calculated by
taking an average over a number of samples. Finally, a ramp is created between
the starting of the draft change operation (green line) and the end of
operation (red line). The slope of the ramp is calculated using the difference
between the draft measurements before and after the draft change operation.
The draft change operation can either be identified manually, by looking at
the time-series plots, or using the steady-state (or stationarity) filter
developed by Dalheim and Steen (2020a).

In case of AIS data, Bailey et al. (2008) reported that 31% of the draft
information out of the investigated AIS messages had obvious errors. The draft
information from AIS data generally corresponds to the condition of ships
while arriving at or departing from the port, and changes due to fuel
consumption and ballast adjustment onboard are rarely updated. Since the draft
obtained from the AIS as well as noon reports has a long update cycle and is
acquired by humans, it is practically difficult to precisely fix the draft
values as in the case of in-service data. However, by comparing the obtained
draft with a reference value, it may be possible to gauge whether the obtained
draft is, in fact, correct. If the obtained draft excessively deviates from
the reference, it may be possible to remove the corresponding data samples
from further analysis or replace the obtained draft value with a more
appropriate value. Table 3 shows the results of investigating the average
draft ratio, which is the ratio of the actual draft ($T_{c}$) and design draft
($T_{d}$), for various ship types from 2013 to 2015 by Olmer et al. (2017). As
summarized in the table, the draft ratio varies depending on the ship type and
the voyage type. By using these values as the above mentioned reference, the
draft obtained from the AIS data and noon reports can be roughly checked and
corrected.

Table 3: Average draft ratio ($T_{c}/T_{d}$) for different ship types. $T_{c}$ = actual draft during a voyage; $T_{d}$ = design draft of the ship. Ship types | Ballast Voyage | Laden Voyage
---|---|---
Liquefied gas tanker | 0.67 | 0.89
Chemical tanker | 0.66 | 0.88
Oil tanker | 0.60 | 0.89
Bulk carrier | 0.58 | 0.91
General cargo | 0.65 | 0.89
The following ship types do not generally have ballast-only voyages.
Container | 0.82
Ro-Ro | 0.87
Cruise | 0.98
Ferry pax | 0.90
Ferry ro-pax | 0.93

###  4.8 Calculate Hydrostatics

Depending on the type of performance analysis, it may be necessary to have
features like displacement, wetted surface area (WSA), etc. in the dataset, as
they are more relevant from a hydrodynamic point of view. Moreover, most of
the empirical or physics-based methods for resistance calculations (to be done
in the next step) requires these features. Unfortunately, these feature cannot
be directly recorded onboard the ship. But it is fairly convenient to estimate
them using the ship’s hydrostatic table or hull form (or offset table) for the
corresponding mean draft and trim for each data sample. Here, it is
recommended to use the corrected draft and trim values, obtained in the
previous step. If the detailed hull form is not available, the wetted surface
area can also be estimated using the empirical formulas shown in table 4. The
displacement at design draft, on the other hand, can be estimated using the
ship particulars and typical range of block coefficient ($C_{B}$), presented
in table 5.

Table 4: Estimation formulas for wetted surface area of different ship types. Category | Formula | Reference
---|---|---
Tanker/Bulk carrier | $WSA=0.99\cdot(\frac{\nabla}{T}+1.9\cdot L_{WL}\cdot T)$ | Kristensen and Bingham (2017)
Container | $WSA=0.995\cdot(\frac{\nabla}{T}+1.9\cdot L_{WL}\cdot T)$ | Kristensen and Bingham (2017)
Other (General) | $WSA=1.025\cdot(\frac{\nabla}{T}+1.7\cdot L_{PP}\cdot T)$ | Molland (2011)
Table 5: Typical block coefficient ($C_{B}$) range at design draft for different ship types, given by Solutions (2018). Category | Type | Block coefficient ($C_{B}$)
---|---|---
Tanker | Crude oil carrier | 0.78-0.83
| Gas tanker/LNG carrier | 0.65-0.75
| Product | 0.75-0.80
| Chemical | 0.70-0.78
Bulk carrier | Ore carrier | 0.80-0.85
| Regular | 0.75-0.85
Container | Line carrier | 0.62-0.72
| Feeder | 0.60-0.70
General cargo | General cargo/Coaster | 0.70-0.85
Roll-on/roll-off cargo | Ro-Ro cargo | 0.55-0.70
| Ro-pax | 0.50-0.70
Passenger ship | Cruise ship | 0.60-0.70
| Ferry | 0.50-0.70

###  4.9 Calculate Resistance Components

There are several components of the ship’s total resistance, and there are
several methods to estimate each of these components. The three main
resistance components which generally constitutes the majority of the ship’s
total resistance are calm-water, added wind, and added wave resistance. It is
possible to further divide the calm-water resistance into sub-components,
namely, skin friction and residual resistance. The total calm-water resistance
can be calculated using one of the many well-known empirical methods, like
Guldhammer and Harvald (Guldhammer and Harvald (1970)), updated Guldhammer and
Harvald (Kristensen and Bingham (2017)), Hollenbach (Hollenbach (1998)),
Holtrop and Mennen (Holtrop and Mennen (1982)), etc. These empirical methods
are developed using the data from numerous model test results of different
types of ships, and each one is proven to be fitting well on several different
ship types. The latter makes choosing the right method for a ship quite
complicated.

The easiest way to choose the right calm-water resistance estimation method is
to calculate the calm-water resistance from each of these methods and
comparing it with the corresponding data obtained for the given ship. The
calm-water data for a given ship can be obtained from the model tests, sea
trial, or even filtering the operational data, obtained from one of the
sources discussed here (in section 3), for near-calm-water condition. The
usual practice here is to use the sea trial data as it is obtained and
corrected for near-calm-water condition and do not suffer from scale effects,
seen in model test results. But the sea trials are sometimes conducted at only
the high range of speed and ballast displacement (as shown in figure 5). Thus,
it is recommended to use the near-calm-water filtered (and corrected)
operational data to choose the right method so that a good fit can be ensured
for a complete range to speed and displacement.

According to ITTC (2017), the increase in resistance due to wind loads can be
obtained by applying one of the three suggested methods, namely, wind tunnel
model tests, STA-JIP, and Fujiwara’s method. If the wind tunnel model test
results for the vessel are available, it may be considered as the most
accurate method for estimating added wind resistance. Otherwise, the database
of wind resistance coefficients established by STA-JIP (van den Boom et al.
(2013)) or the regression formula presented by Fujiwara et al. (2005) is
recommended. From the STA-JIP database, experimental values according to the
specific ship type can be obtained, whereas Fujiwara’s method is based-on the
regression analysis of data obtained from several wind tunnel model tests for
different ship types.

The two main sets of parameters required to estimate the added wind resistance
using any of the above three methods are incident wind parameters and
information regarding the exposed area to the wind. The incident wind
parameters, i.e., relative wind speed and direction, can be obtained from
onboard measurements or weather hindcast data. In case of weather hindcast
data, the relative wind measurements can be calculated from the hindcast
values according to the formulation outlined by ITTC (2017) in section E.1,
and in case of onboard measurements, the relative wind measurements should be
corrected for the vertical position of the anemometer according to the
instructions given by ITTC (2017) in section E.2, also explained here in
section 4.5. The information regarding the exposed area to the wind can be
either estimated using the general arrangement drawing of the ship or
approximately obtained using a regression formula based-on the data from
several ship, presented by Kitamura et al. (2017).

The added wave resistance ($R_{AW}$) can also be obtained in a similar manner
using one of the several well-established methods for estimating $R_{AW}$.
ITTC (2017) recommends conducting sea keeping model tests in regular waves to
obtain $R_{AW}$ transfer functions, which can further be used to estimate
$R_{AW}$ for the ship in irregular seas. To empirically obtain these transfer
functions or $R_{AW}$ for a given ship, it is possible to use physics-based
empirical methods like STAWAVE1 and STAWAVE2 (recommended by ITTC (2017)).
STAWAVE1 is a simplified method for directly estimating $R_{AW}$ in head wave
conditions only, and it requires limited input, including ship’s waterline
length, breadth, and significant wave height. STAWAVE2 is an advanced method
to empirically estimate parametric $R_{AW}$ transfer functions for a ship. The
method is developed using an extensive database of sea keeping model test
results from numerous ships, but unfortunately, it only provides transfer
functions for approximate head wave conditions (0 to $\pm$45 degrees from
bow). A method proposed by DTU (Martinsen (2016); Taskar and Andersen (2019);
Taskar and Andersen (2021)) provides transfer functions for head to beam seas,
i.e., 0 to $\pm$90 degrees from bow. Finally, for all wave heading, it may be
recommended to use the newly established method by Liu et al. (2020). There
have been several studies to assess and compare the efficacy of each of these
methods and several other methods, but no consistent guidelines are provided
regarding their applicability.

###  4.10 Data Cleaning & Outlier Detection

It may be argued by some that the process of data cleaning and outlier
detection should be carried-out way earlier in the data processing framework,
as proposed by Dalheim and Steen (2020b), but it should be noted here that all
the above steps proposed here have to be performed only once for a given
dataset, whereas data cleaning is done based on the features selected for
further analysis. Since the same dataset can be used for several different
analyses, which may be using different sets of features, some part of data
cleaning has to be repeated before each analysis to obtain a clean dataset
with as many data samples as possible. Moreover, the additional features
acquired during the above listed processing steps may be helpful in
determining to a better extent if a suspected sample is actually an outlier or
not.

Nevertheless, it may be possible to reduce the work load for the above
processing steps by performing some basic data cleaning before some of these
steps. For instance, while calculating the resistance components for in-trip
data samples, it is possible to filter-out samples with invalid values for one
or more of the ship data variables used to calculate these components, like
speed-though-water, mean draft (or displacement), etc. This would reduce the
number of samples for which the new feature has to be calculated. It should
also be noted that even if such simple data cleaning (before each step) is not
performed, these invalid samples would be easily filtered-out in the present
step. Thus, the reliability and efficacy of the data processing framework is
not affected by performing the data cleaning and outlier detection step at the
end.

Most of the methods developed for ship performance monitoring assumes that the
ship is in a quasi-steady state for each data sample. The quasi-steady
assumption indicates that the propulsive state of the ship remains more or
less constant during the sample recording duration, i.e., the ship is neither
accelerating nor decelerating. This is specially critical for aforementioned
time-averaged datasets, as the averaging duration can be substantially long,
hiding the effects of accelerations and decelerations. Here, the two-stage
steady-state filter, explained in section 4.3, can be applied to the shaft rpm
time-series to remove the samples with accelerations and decelerations,
resulting in quasi-steady samples. In tandem to the steady-state filter on the
shaft rpm time-series, it may also be possible to use the steady-state filter,
with relaxed setting, on the speed-over-ground time-series to filter-out the
sample where the GPS speed (or speed-over-ground) signal suddenly drops or
recovers from a dead state, resulting in measurement errors.

As discussed in section 3.1.2, the outliers can be divided into two broad
categories: (a) Contextual outliers, and (b) Correlation-defying outliers. The
contextual outliers can be identified and resolved by the methods presented as
well as demonstrated by Dalheim and Steen (2020b), and for correlation-defying
outliers, methods like Principal Component Analysis (PCA) and autoencoders can
be used. Figure 8 shows the in-service data samples recorded onboard a ship.
The data here is already filtered-out for quasi-steady assumption, explained
above, and contextual outliers, according to the methods suggested by Dalheim
and Steen (2020b). Thus, the samples highlighted by red circles (around 6.4 MW
shaft power in figure 8(a)) can be classified as correlation-defying outliers.
The time-series plot (shown in figure 8(b)) clearly indicates that the
detected outliers have faulty measurements for the speed-through-water (stw)
and speed-over-ground (sog), defying the correlation between these variables
and the rest. It is also quite surprising to notice that the same fault occurs
in both the speed measurements at the same time, considering that they are
probably obtained from different sensors.

(a) Log speed (or stw) vs shaft power.

(b) Time-series.

Figure 8: Correlation-defying outliers marked with red circles.

##  5 Conclusion

The quality of data is very important in estimating the performance of a ship.
In this study, a streamlined semi-automatic data processing framework is
developed for ship performance analysis. The data processing framework can be
used to process data from several different sources, like onboard recorded in-
service data, AIS data and noon reports. These three data sources are
discussed here in detail along with their inherent problems and associated
examples. It is here recommended to use the onboard recorded in-service data
for ship performance monitoring over the other data sources, as it is
considered more reliable due its consistent and higher sampling rate.
Moreover, the AIS data and noon reports lacks some of the critical variables
required for ship performance analysis, and they are also susceptible to human
error, as some of the data variables recorded here are manually logged by the
ship’s crew. Nevertheless, all three data sources are known to have several
problems and should be processed carefully for any further analysis.

The data processing framework, presented in the current work, is designed to
address and resolve most of the problems found in the above three data
sources. It is first recommended to divide the data into trips so that further
processing can be performed in a more systematic manner. A simple logic to
divide the data into individual trips is outlined here if the port call
information is not available. The weather hindcast (metocean) data is
considered as an important supplementary information, which can be used for
data validation and estimating environmental loads experienced by the ship. A
simple algorithm to effectively interpolate the hindcast data at a specific
time and location of a ship is presented within the data processing framework.
The problem of erroneous draft measurements, caused due to the Venturi effect,
is discussed in detail as well as simple interpolation is recommended to fix
these measurements. A more complex case, where the draft or trim is
voluntarily adjusted during the voyage without reducing the vessel speed, is
also presented here. Such a case cannot be resolved with simple interpolation,
and therefore, an alternate method is suggested for the same problem.

Choosing the most suitable methods for estimating resistance components may
also be critical for ship performance analysis. It is, therefore, recommended
to carry out some validation checks to find the most suitable methods before
adopting them into practice. Such validation checks should be done, wherever
possible, using the data obtained from the ship while in-service rather than
just using the sea trial or model test results. Data cleaning and outlier
detection is also considered an important step for processing the data. Since
cleaning the data requires selecting a subset of features relevant for the
analysis, it is recommended to perform this as the last step of the data
processing framework, and some part of it should be reiterated before carrying
out a new type of analysis. The presented data processing framework can be
systematically and efficiently adopted to process the datasets for ship
performance analysis. Moreover, the various data processing methods or steps
mentioned here can also be used elsewhere to process the time-series data from
ships or similar sources, which can be used further for a variety of tasks.

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