Deep-Argo Otarriinae profiling float is a new type of Argo profiling float that has a maximum diving depth of more than 4,000 m. It can collect ocean scientific data all-weather and uninterruptedly, which provides reliable data support for the global ocean scientific research. The working time of Deep-Argo profiling float is an important indicator of its practicality and economy, and it is clear that the energy consumption is a key factor in determining its working time. In this paper, the single profile energy consumption model with 19 parameters of Deep-Argo Otarriinae is established and the main effect indices and total effect indices of the energy consumption parameters to energy consumption are calculated using Sobol’ sensitivity analysis method, aiming to find the parameters that have the greatest impact on energy consumption. The results show that the gliding angle, the diving depth, and the gliding speed have a significant impact on energy consumption of Deep-Argo Otarriinae. The results of simulation have a good match with the actual application and have certain reference significance for the determination of the design parameters and the selection of the navigation parameters. This paper also provides a new idea of multiparameter energy consumption modeling for underwater equipment using buoyancy regulation.
Argo profiling float is a typical type of ocean observation platform, which provides continuous observations of ocean temperature and salinity versus pressure, from the sea surface to the maximum design depth of 2,000 m [
Deep-Argo Otarriinae profiling float is a new type of Argo profiling float that has a maximum diving depth of more than 4,000 m while the conventional one has a maximum diving depth of 2,000 m. Deep-Argo extends the observation range of Argo profiling float to the sea floor and accurately measures variation of seawater parameters in the deep sea areas [
In this paper, the 4,000 m Deep-Argo Otarriinae profiling float developed by Shandong University is regarded as the research object [
4000 m Deep-Argo Otarriinae developed by Shandong University.
The Deep-Argo Otarriinae profiling float developed by Shandong University is mainly composed of pressure chamber, hydraulic system, communication and positioning unit, embedded control system, and sensors. The pressure chamber provides a sealed and waterproof environment for the internal subsystem. The hydraulic system adjusts the volume of Deep-Argo Otarriinae by controlling the hydraulic oil to flow in or flow out the outer oil bladder to achieve buoyancy adjustment. The communication and positioning unit is mainly composed of a global positioning system, Iridium communication module, and wireless communication module. Deep-Argo Otarriinae can switch the communication mode according to the distance between Deep-Argo Otarriinae and the shore station and the mission demand. The embedded control system manages tasks in real time, performs status monitoring, and data analysis. The sensors are responsible for monitoring the operational status and data acquisition of the Deep-Argo Otarriinae profiling float.
The general single profile workflow of Deep-Argo Otarriinae is shown in Figure
The general single profile workflow of Deep-Argo Otarriinae.
The simplified single profile workflow of Deep-Argo Otarriinae.
The operating state of each subsystem in a single profile.
Before building an energy consumption model, we need to find out the relationship between the parameters of Deep-Argo Otarriinae. The kinetic parameters and force analysis of Deep-Argo Otarriinae during steady gliding are shown in Figure
Steady gliding state of Deep-Argo Otarriinae.
The geometric relationships and force balance relationships of the steady gliding motion can be expressed as
The drag force and lift force of Deep-Argo Otarriinae can be expressed as
Applying the drag force and lift force obtained by equation (
It can be seen from equation (
Combining the single profile workflow of Deep-Argo Otarriinae and the operating state of each subsystem, the energy consumption analysis of each subsystem is performed, respectively. As shown in Figure
The energy consumption of hydraulic system mainly includes the energy consumption of the servo motor and the solenoid valve. There are two buoyancy adjustment stages in a single profile workflow, which are diving preparation stage and ascending preparation stage. In the diving preparation stage, the hydraulic oil is driven to the inner oil bladder from outer oil bladder by the plunger pump on the sea surface, the volume of the outer oil bladder will shrink, and buoyancy force on the equipment will decrease, so Deep-Argo Otarriinae starts to dive. Conversely, in the ascending preparation stage, the hydraulic oil is driven to the outer oil bladder from inner oil bladder by the plunger pump, the volume of the outer oil bladder will swell, and buoyancy force on the equipment will increase, so Deep-Argo Otarriinae starts to ascend. The hydraulic schematic diagram of Deep-Argo Otarriinae is shown in Figure
The hydraulic schematic diagram of Deep-Argo Otarriinae.
Total energy consumption of the hydraulic system in a single profile can be described as
Equation (
From equations (
According to the relationship between the buoyancy and the volume change, the following equation can be obtained easily:
By substituting equations (
Since Deep-Argo Otarriinae completes the communication and positioning process on the sea surface, the energy consumption in this process is only related to the power and running time of relevant electronic equipment and has no obvious relationship with the navigation parameters and design parameters of Deep-Argo Otarriinae. Energy consumption generated by positioning and communication unit in a single profile can be described as
Deep-Argo Otarriinae profiling float can be equipped with a variety of sensors. Sensors can be divided into two types based on different operating modes: full-range operating sensors and intermittent operating sensors. The sensors embedded in our prototype are shown in Table
Sensors embedded in Deep-Argo Otarriinae
Full-range operating sensors | Sensors controlled by depth | CTD |
---|---|---|
Pressure transmitter | Altimeter | SBE 37-SMMicroCAT CT(P) recorder |
Linear displacement sensor |
The full-range operating sensors mean that sensors operate throughout the single profile (excluding the communication and waiting stage). For example, the pressure transmitter monitors the change of pressure throughout the whole workflow. The CTD embedded in our prototype is SBE 37-SMMicroCAT CT(P) Recorder which is self-contained. The sampling interval of CTD is 6 s to 6 h, and the sampling time is 1.8 s to 2.6 s. The energy carried by CTD can collect 960,000 data. The energy consumed by CTD is only used to read the data collected by CTD and not to drive the pump and electronic components inside CTD. According to the specifications of the Argo organization, CTD is not open all the way, but only during ascending stage. In the simplified workflow of Deep-Argo Otarriinae, the buoyancy adjustment and hydrodynamic coefficient of Deep-Argo Otarriinae are basically the same in the diving stage and ascending stage. In other words, the values of the factors that affect the speed of ascent and descent are similar, so the speed of ascent and descent is basically the same and the time of the diving stage and ascending stage is almost identical. In order to facilitate the calculation, we include CTD in the full-range operating sensors. The energy consumption of the full-range operating sensors can be described as
The intermittent operating sensors mean that sensors operate at regular depth intervals in order to save energy or to meet measurement requirements. The specific sampling process of intermittent operating altimeter is shown in Figure
The specific sampling process of intermittent operating altimeter.
The embedded control system keeps working during the entire profile, including the communication and waiting stage. The energy consumption of this part can be described as
In summary, the total energy consumption of control system and sensors can be described as
The total energy consumption model in a single profile can be obtained by adding the energy consumption of each part mentioned above, which can be described as
The energy consumption model of Deep-Argo Otarriinae in a single profile has the following characteristics: There are many parameters involved, including hydrodynamic parameters, hydraulic system parameters, navigation parameters, main design parameters, and other 19 parameters. There is a coupling relationship between the energy consumption of each subsystem. The energy consumption of each subsystem in the model is related to multiple parameters, and changes in some parameters will lead to changes of multiple subsystems in energy consumption. The energy consumption model is highly nonlinear.
Some parameters are not determined in the design of Deep-Argo Otarriinae. Their values will show a certain change law with the change of working environment, so they need to be obtained through experiment or simulation. Another part of the parameters are determined in the design and their parameter values are shown in Table
Parameters determined in the design.
Parameters | Value | Unit symbol |
---|---|---|
0.107 | ||
0.01 | W | |
1 | ||
1 | ||
1.92 | ||
1025 | ||
9.8 |
As shown in Figure
Hydraulic booster system for testing.
Through the test of Deep-Argo Otarriinae hydraulic system, we finally obtained the power of hydraulic system in the diving preparation stage and ascending preparation stage as shown in Figure
Power of hydraulic system in the test. (a) Volume change of external oil bladder in the diving preparation stage. (b) Power of hydraulic system in the ascending preparation stage.
It can be seen from Figure
According to the fitting results, the complex correlation coefficient
The flow of the hydraulic system in the test is shown as Figure
Flow of hydraulic system in the test. (a) Diving preparation stage. (b) Ascending preparation stage.
From Figure
The power and flow of hydraulic system is determined by the performance and design parameters of the system, which can be considered as a fixed value and sensitivity analysis is not required.
There are several methods that will produce results for hydrodynamic parameters based on a given geometry. The methods include analytical, experimental, computational, and semiempirical approaches [
Results for hydrodynamic parameters.
Hydrodynamic parameters | ||||
---|---|---|---|---|
Value | 23.8 | 1156.1 | 0.1056 | 44.4792 |
The hydrodynamic parameters are necessary and important to measure the hydrodynamic performance of Deep-Argo Otarriinae. The variation of the hydrodynamic parameters has a very important impact on the energy consumption and voyage of Deep-Argo Otarriinae, so sensitivity analysis for hydrodynamic parameters is needed. For the convenience of analysis, we assume that each hydrodynamic coefficient can fluctuate by 20% compared with the prototype and follows the uniform distribution within the respective value range.
The navigation parameters are arguments that the operator needs to set directly or indirectly and are also the key to measure the underwater operation state of Deep-Argo Otarriinae. Therefore, it is necessary to study the influence of navigation parameters on the energy consumption and voyage of Deep-Argo Otarriinae. Gliding speed The gliding speed of the Deep-SOLO float is about 0.06 m/s, the gliding speed of the Deep-SOLO 2 float is about 0.12 m/s, and the gliding speed of the Arvor-C profiling float is about 0.15–0.20 m/s [ Gliding angle According to equation ( By substituting equations ( The attack angle We stipulate that the gliding angle of Deep-Argo Otarriinae is within Substituting the hydrodynamic parameters shown in Table Diving depth The diving depth of Deep-Argo Otarriinae is determined by the operator. The diving depth of Deep-Argo Otarriinae ranges from 0 to 4,000 m, and Communication and waiting time Since the satellite signal intensity will be affected by weather condition, marine environment, satellite operating state, and other factors, and the operator may perform additional data exchange operations with Deep-Argo Otarriinae according to the task requirements, the communication and waiting time will have a certain randomness. As a matter of experience, positioning and communication time Intermittent operating sensors opening depth interval The intermittent operating sensor carried by Deep-Argo Otarriinae is only an altimeter that prevents Deep-Argo Otarriinae from bottoming out. Too small opening depth interval of altimeter will greatly increase energy consumption while too large opening depth interval will easily cause Deep-Argo Otarriinae bottom out. Considering the diving speed of Deep-Argo Otarriinae and the buoyancy adjustment time, we set the altimeter opening depth interval
Sensitivity analysis (SA) aims to identify the key parameters that affect model performance, and it plays important roles in model parameterization, calibration, optimization, and uncertainty quantification [
Sobol’ method estimates the importance of each input parameter by means of variance decomposition [
Assuming that the square of
The left part of equation (
Each term on the right side of equation (
The joint effect of input parameters on the model output can be described as
The main effect indices
The difference between the main effect and the total effect indices of the parameter
Since the energy model established in this paper is complex and some parameters are constant, it is impossible and unnecessary to perform sensitivity analysis on each parameter. Therefore, only the parameters most concerned by the researchers are selected for sensitivity analysis. In Section
Parameters distribution range and distribution law.
Parameters | Minimum value | Maximum value | Unit symbol | Distribution |
---|---|---|---|---|
19.04 | 28.56 | kg/m | Uniform | |
924.88 | 1387.32 | kg/m | Uniform | |
0.0845 | 0.1267 | kg/m | Uniform | |
53.3750 | 35.5834 | kg/m | Uniform | |
0.05 | 0.20 | m/s | Uniform | |
-7.76 | 7.51 | Deg | Uniform | |
200 | 4000 | M | Uniform | |
600 | 1200 | S | Uniform | |
0 | 50 | M | Uniform | |
2 | 10 | S | Uniform |
The number of independent parameters
Results for main effect indices of each parameter with model evaluations.
Results for total effect indices of each parameter with model evaluations.
In Figures
Results of the mean values for main effect and total effect with Sobol’ method.
Total effect and main effect of each energy consumption parameter.
Order | Parameters | Total effect | Main effect |
---|---|---|---|
1 | 0.6745 | 0.3112 | |
2 | 0.4325 | 0.1325 | |
3 | 0.2789 | 0.0852 | |
4 | 0.0511 | 0.0118 | |
5 | 0.0508 | 0.0109 | |
6 | 0.0507 | 0.0097 | |
7 | 0.0507 | 0.0098 | |
8 | 0.0505 | 0.0097 | |
9 | 0.0501 | 0.0121 | |
10 | 0.0469 | 0.0115 |
Analysis and discussion about the above simulation results are given as follows: Within the range of parameters studied in this paper, the gliding angle Among the three key parameters that affect the energy consumption, the diving depth In order to reduce the energy consumption of Deep-Argo Otarriinae, for designers, the simulation results above point out the optimization direction in the design process. Designers should focus on reducing the glide angle and the gliding speed through a large number of prototype pool experiments and hydrodynamic simulation. For operators, the simulation results show the influence of diving depth on energy consumption mathematically. When there is no mandatory requirement for the diving depth, operators should select the diving depth reasonably.
In this paper, a new modeling method for multiparameter energy consumption model of Deep-Argo Otarriinae was proposed. First, the kinematics model of Deep-Argo Otarriinae was established to show the relationship between various parameters. Then, the energy consumption of each subsystem of Deep-Argo Otarriinae in a single profile was calculated. Finally, an energy consumption model including hydraulic system parameters, navigation parameters, and other 19 parameters was established, which could describe the energy consumption of Deep-Argo Otarriinae in a single profile accurately and comprehensively. The energy consumption model we proposed contains many parameters and is highly nonlinear, which has certain research value and provides a new idea of multiparameter energy consumption modeling for underwater equipment using buoyancy regulation because their energy consumption components are similar. To reduce energy consumption of Deep-Argo Otarriinae and extend its working time, the Sobol’ method was introduced to analyze the sensitivity of energy consumption parameters and the main effect indices and total effect indices of the selected parameters to energy consumption were calculated. The results of sensitivity analysis show that the gliding angle
Future work can be done by establishing a more accurate kinematics model which incorporates more parameters and obtaining the optimal solution for hydrodynamic coefficients and gliding speed in the design. Furthermore, we can study the relationship between energy consumption and diving depth or gliding speed to lay the foundation for further research on reducing energy consumption of Deep-Argo Otarriinae.
The data used to support the findings of this study are included within the article.
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Weiwei SI and Yifan XUE contributed equally to this article.
This paper was supported by the Key Research and Development Program of Shandong Province (NO. 2019GHY112077), the Guangdong Basic and Applied Basic Research Foundation (NO. 2019A1515110040), the Research Fund of State Key Laboratory of Ocean Engineering (Shanghai Jiaotong University) (NO. 1911), the Shandong Province Postdoctoral Innovation Project (NO. 201901001), the Laboratory for Marine Geology, Qingdao National Laboratory for Marine Science and Technology (NO. MGQNLM201806), the Shenzhen Science and Technology R&D Foundation (NO. JCYJ20180305164217766), and the Qingdao Postdoctoral Applied Research Project. Gang Xue is the visiting research fellow of State Key Laboratory of Ocean Engineering. Shenzhen Research Institute of Shandong University is the primary supported department.