Diagnostic structure of visual robotic inundated systems with fuzzy clustering membership correlation

Novelty

The entire design of robotic system in proposed method is made using a novel mathematical model which is arranged into separate clusters. For each cluster (fuzzy membership function) the data is transmitted to control center which describes the current state operation of underwater systems. Once the data is transmitted by several clusters then hierarchical procedure is followed for arranging entire data segments in proper format thereby ensuring appropriate metrics for each transmitted data. Moreover the major novelty of projected model is to maximize the detection range of robots that is present at underwater systems. In addition as compared to existing models applicable point of detection is made by robotic systems thus time period of monitoring is reduced. Further the relationship in terms of analytical parameter which is made with respect to distinct subsurface area provides precise fuzzy membership function. The above mentioned fuzzy membership function in proposed method is calculated by considering the functions for first and last node points.

Major contributions

To provide solutions for aforementioned research gap in the field of robotics for underwater communication the proposed method is incorporated by using a cluster node at various points deep inside the concentration levels where every data at control centre is transmitted by using fuzzy logic controller that provides the advantage of clustering in underwater communications. The novelty of the projected model depends on measuring all parameters that can be either minimized or maximized.

• To design the robotic system that can able to provide maximized communication ranges for data transmission after identifying corresponding targets.

• To maximize the performance of robotic systems where improbable values are reduced by measuring accurate points (in terms of identification and node implementations).

• To reduce the overlap conditions of installed nodes by using fuzzy clustering algorithm thereafter maximizing the energy ranges at each node points to provide uninterrupted data about underwater systems.

Article organization

The remaining section of the article is organized as follows, “Proposed system model” provides detailed mathematical model for proposed robotic system. “Methods/Experimental” integrates the designed robotic system with fuzzy membership function and data path measurements are made using clustering phases. “Results and discussion” simulates the outcome of proposed method with comparison cases. Finally the conclusion is provided with limitations and directions for future work.

Proposed system model

A special framework design is required for underwater systems in order to reduce operational complexity. Therefore, the operational conditions of robotic systems using sensor modules are provided along with an IoT framework in this part. To avoid errors that occur during the installation’s initial phase, measurements are conducted precisely when defining the analytical terms. Furthermore, if a robotic model is represented, specific parameters derived from Eq. (1) must be used to define the robot’s communication range.

(1) $$C_i=max\sum _{i=1}^n\left(N_i-T_i\right)$$where,

$N_i$ denotes the installed node module.

$T_i$ indicates target in underwater systems.

The difference between the installed node and the matching target, which needs to be maximized over a specific distance, is represented by Eq. (1). Since Eq. (2) can be used to measure the performance of robotic tools, some positions must be tested using this range.

(2) $$P_i=max\sum _{i=1}^n{I}_i\ast \left(U_i-U_1\right)$$where,

$I_i$ describes the input parametric values.

$U_i$, $U_1$ denotes improbability values of robotic measurements.

The second objective function, which must be maximized using an input parameter and a set of unknown measurements, is represented by Eq. (2). Equation (3) can be used to define a node parameter as follows to prevent uncertain measurements,

(3) $$M{N}_i=\sum _{i=1}^n{\displaystyle \frac{T{N}_i}{R{N}_i}\ast 100}$$where,

$T{N}_i$ indicates total number of nodes installed in underwater.

$R{N}_i$ denotes minimum number of node coverage in defined radius.

Equation (3) calculates the percentage of the system’s total uncertain periods that are avoided when compared to uncertain measurement data. However, if the installed nodes overlap, the concentration in the robotic network will be low and needs to be optimized using Eq. (4), as stated below,

(4) $$densit{y}_i=max\sum _{i=1}^n{\displaystyle \frac{V_i}{P_i}}$$where,

$V_i$ indicates the volume of node.

$P_i$ denotes individual node partition.

The concentration range of the robot will expand in underwater systems as additional nodes are divided, resulting in the proper energy consumption, which is described using Eq. (5) as follows,

(5) $$Energ{y}_i=max\sum _{i=1}^n{\tau }_i\ast d_t\left(i\right)\ast {\rho }_i$$where,

${\tau }_i$ denotes supplied power for robotic operation.

$d_t$ indicates time required by a robot for data transmission.

${\rho }_i$ represents robotic network transmission distance.

Equation (5) depicts the period of operation at maximum efficiency, during which the issue of more power causes an increase in the likeness ratio, which can be characterized using Eq. (6) as follows,

(6) $$L_i=\sum _{i=1}^n{\displaystyle \frac{S{S}_b\left(i\right)}{S{S}_a\left(i\right)}\ast 100}$$where,

$S{S}_b$, $S{S}_a$ denotes subsurface area that is present at both levels in underwater systems.

Equation (7) can be used to express the overall time required to provide acceptable service using the complete network and nodes. The likeness ratio as mentioned in Eq. (6) must be normalized with regard to the motions of the robot.

(7) $$Tim{e}_i=\sum _{i=1}^n{m}_t\left(i\right)+{\beta }_t\left(i\right)+{\phi }_i$$where,

$m_t$ indicates mean time period.

${\beta }_t$ represents time taken for robot envisioning from underwater.

${\phi }_i$ denotes cyclic time periods.

Using signaling systems with an inter-arrival rate, the whole time of the robotic system may be observed, resulting in a significantly shorter representation time than would be anticipated. Equation (8) can be used to express the objective function by merging the full analytic framework.

(8) $$ob{j}_i=max\sum _{i=1}^n{C}_i,P_i,densit{y}_i,Energ{y}_i$$

For expanding the monitoring communication range, the density of monitoring in subsea systems, the applied power for monitoring, and the energy of node systems, the objective function defined in Eq. (8) is a maximization framework. However, an integration segment with an optimization method is necessary for underwater testing and is explained in “Research gap and motivation” in order to maximize the effectiveness of the suggested technique. In the proposed method there are four different control variables as provided in the objective functions where if the considered parameters fails to function effectively then the robotic system cannot able to monitor the condition of underwater systems thereby no information can be achieved at receiver. To prevent the failure of robotic functionalities communication range at each node point is identified and the information is provided to control centres. Hence the major significance on identifying communication distance is that it is possible to identify the target values thereafter achieving information about targets in a much easy way. The secondary importance is provided on determining the robotic positions where if the robotic system does not move with respect to considered node points then precise information can never be achieved about types of objects that is present deep inside. In addition to distance and movement that is considered for data and device the functionalities are performed with concentration and energy factors where deep inside the water the robotic device must not waste high energy for performing single operation.

Methods/Experimental

Some characteristic acts that need to be conducted to analyze the impact of underwater robotic systems are represented using a fuzzy algorithm and clustering technique. The main benefit of using the fuzzy technique is that it helps underwater systems solve their low computing complexity problem. Even if most automated algorithms exist to reduce complexity, such as machine learning, deep learning, and artificial intelligence, the fuzzy clustering algorithm gives data points in accordance with robots’ gradual movements. Therefore, for the aforementioned benefit, the fuzzy clustering technique is combined with the suggested system model so that numerous movements of underwater objects may be easily detected. Other communication units are not required in the representation scenarios due to the flexibility of data points being expanded above the stated ranges. In addition, fuzzy offers a hard clustering of data points with precise membership functions in comparison to other clustering methods (Al-ani et al., 2023; Selvarajan & Manoharan, 2023). As a result, Eq. (9) may be used to define the data membership function as follows,

(9) $$D{M}_i=min\sum _{i=1}^n{\left(y_i-z_i\right)}^2$$where,

$y_i$, $z_i$ represents mean membership functions with value greater than 1.

Euclidian distance is represented for data points using an iterative membership function in Eq. (9) minimization function. However, as shown in Eq. (10), the mean sample values of robotic movement must be measured using a weight matrix.

(10) $$W_i=\sum _{i=1}^n{e}^{\left(mea{n}_i-mea{n}_1\right)}\ast {\gamma }_i$$where,

$mea{n}_i$, $mea{n}_1$ denotes mean values of first and last nodes.

${\gamma }_i$ represents robot weight classification matrix.

In order to reduce the sensitivity of the data prediction system from the associated robot, the exponential values in Eq. (10) must be partitioned in a certain way. As a result, as defined in Eq. (11), metrics assessments are performed within the boundary regions with a defined surrounding set.

(11) $$metric{s}_i=max\sum _{i=1}^n\left({\omega }_i+{\vartheta }_i\right)$$where,

${\omega }_i$ denotes number of neighboring nodes.

${\vartheta }_i$ represents total number of robotic system.

Therefore the total objective function is modified by adding the metrics values as indicated in Eq. (12).

(12) $$modob{j}_i=max\sum _{i=1}^{n}ob{j}_i+metric{s}_i$$

The combined programming loop codes can be framed using Eq. (12) where the implementation flow chart is provided in Fig. 2.

Step-by-step implementation of fuzzy clustering with robotic underwater systems

Input parameters.

$D=u(1);$

$y=u\left(2\right);$

$c=-5$; /Initial communication range

$c_1=3.9$; /Modified communication range (Proposed method)

Command parameters

$L_1=18$; /Detection of obstacles at first state

$L_2=18$; /Detection of obstacles at second state

$L_1=\sqrt{D^2+y^2}$;

$k=\sqrt{c^2+{c_1}^2}$;

$v=a\tan \left(\frac{y}{D}\right);\text{}/\text{Measurement\hspace{0.17em}\hspace{0.17em}of\hspace{0.17em}\hspace{0.17em}density\hspace{0.17em}\hspace{0.17em}ranges}$

$u=a\tan \frac{c1}{c}$;

$u_1=\frac{\pi }{2-u}$;

$v_1=\frac{\pi }{2+y+u}$; /Target nodes

$L=\sqrt{k^2+L_1^2}-2k{L}_1\cos v_1$

if {

$v<u_1$

$an{g}_1={\displaystyle \frac{\pi -a\cos \left(L_1^2\right)}{2L_1}-{\displaystyle \frac{a\cos \left(k^2+L_1^2\right)}{2L_{1}k}-u}}$; /Membership functions

$an{g}_{11}=an{g}_1\times {\displaystyle \frac{180}{\pi }}$

end

}

if {

$v>u_1$

$an{g}_2={\displaystyle \frac{-\pi -a\cos \left(L_1^2\right)}{2L_1}+{\displaystyle \frac{a\cos \left(k^2+L_1^2\right)}{2L_{1}k}-u}}$; /Membership functions with mean values

$an{g}_{22}=an{g}_1\times {\displaystyle \frac{180}{\pi }}$

end

}

$y\left(1\right)=an{g}_{11}$;

$y\left(2\right)=an{g}_{22}$

Scenario 1: range of robotic communication

The communication range and data transfer must be enhanced when a robotic system is created for underwater operation by selecting the object targets properly. Utilizing the node modules already installed, moving nodes can be scheduled using robotic systems. The communication range can be increased to some extent once the long-range sensing units are fitted; however, the initial sensing radius is kept at around 50 m. As a result, the range is maximized, and an IoT module is employed to report the data to the control center. However, the majority of robotic systems are set up to optimize only the connectivity modules and fail to select the proper target. However, the projected method will maximize the communication range due to the distinction between the node modules and the designated target, making precise monitoring always possible at a distance. A simulated examination of communication range with specified targets is shown in Fig. 4 and Table 4.

Scenario 2: measurement of underwater density

The amount of uncertainty that is represented by the suggested method is minimized as the coverage radius is specified at earlier stages and is maximized. Thus, the density of robotic nodes in underwater systems is observed after the quantity of uncertainty has been reduced. With input parametric values set to 1,000 kg/m³, an analysis is conducted to determine the density of submerged creatures. Thus, the excitation levels of underwater robotic restraints are monitored using the density values given above. The density of monitoring is maximized to some extent as the depicted input values are recreated with unlikely robotic readings. It is impossible to wander in any intermediate directions since the body consumption of robotic systems is designed with heavy components. As a result, measurements and simulations are carried out while lowering the improbability values, as shown in Fig. 5 and Table 5.

Scenario 3: maximization of energy

During the course of underwater testing, where the concentration ranges are significantly altered for predetermined limitations, the power supplied for robotic operation is raised. It is required to use certain time period measurements to check the network transmission distance and data transmission during this adjustment. Therefore, the energy usage of robotic systems is tracked and must be maximized across all operational phases. As a result, the network transmission distance that is present deep inside underwater systems will be duplicated in order to measure the energy states during the operating period and supply input power. The extra power supplied to the complete robot during the process of measuring the energy representation values must be examined at various levels of the sea surface. The likeness ratio must therefore be defined at specific concentration ranges by preventing additional power from crossing the threshold values and the comparison outcomes for scenario 3 is indicated in Fig. 6 and Table 6.

Scenario 4: monitoring time periods

The underwater robotic systems must notify the authorities of the status of the necessary parameters within the allotted time frame. When a robotic device is placed, automatic monitoring of all parametric representations is made possible. Intelligent gadgets typically just detect the amount of water existing beneath the sea’s surface. However, some parametric analyses will require some time before they can directly provide the data. Therefore, each central control center is divided into a number of robotic systems that are put in certain spaces. As a result, data collection and relevant action may be done more quickly. Cyclic rotation is taken into account while measuring the time periods in the suggested method since cyclically driven events are described. The sum of the cyclic, average time periods for the operation and prediction stages is used to get the total time period. The time span for automated measurements is shown in Fig. 7 and Table 7.

Scenario 5: score metrics

In this scenario, performance measures for the proposed robotic system are presented and expressed as a total objective function that is added up with results from earlier scenarios. Individual case studies are created as a result, and using fuzzy systems’ gradient functions, they are transformed into metrics scores. In order to examine the model, two distinct membership functions are established using variable representations; as a result, the total score metrics of the robotic system will be maximized if the mean value crosses 1. Exponential function relationships between two mean variables are considered from the final and earliest phases to provide very precise measurement data. As a result, different scores are obtained by reproducing the exponential values with different weight functions. However, the intended robot is built using an equal weight function in the proposed method, which limits the simulation of the metrics to a single run time. Simulated metrics for new and existing approaches are shown in Fig. 8 and Table 8.

Measurement case 1

Whenever a fuzzy system which is operated with hierarchical clustering algorithm then, memory space during data transfer state is highly increased. Hence the operational memory states of fuzzy system for underwater operation are determined in this measurement case. As long the fuzzy membership function is computed the space complexity of the robotic system will be determined. In the projected method space complexity is determined by input measurements where a set of quantities are segregated and organized with final value extents. Further the best, worst and average working functionalities are described with space complexities using upper and lower bound constraints. Hence the analytical representations for space complexity can be represented using big-theta where positive constraints are deliberated. Figure 9 and Table 9 illustrates the space complexity of proposed and existing methods.

Measurement case 2

The amount of resources that is provided for robotic operation which is classified using fuzzy membership function is described in this measurement case. In addition with allocation of resources it is necessary to check the limits of operation in order to ensure stable operation. Hence the computational complexity is examined with elementary operational cases where variation in input size is made to avoid worst complexity cases. If a system provides optimized computational capacity then feasibility design can be guaranteed with respect to exponential time period. In case if a system exhibits more complexity is parametric simulation then external resources can be allocated to solve computational complexities. Figure 10 and Table 10 provides measurement of computational complexities for proposed and existing methods.

Measurement case 3

The robustness of designed robotic device for underwater communication must be examined in a certain way in order to analyse the failure node areas and in addition the robustness of supporting system (fuzzy membership functions) is also monitored with variations of vest epoch conditions. One of the major reason for analysing the robustness conditions is that the underwater communication must tolerate varying changes that are related to underwater environmental conditions. Moreover for communication process estimation it is essential to find a local node point therefore the robotic device which is present deep inside the water can able to establish valuable communication paths. In case if the nodes that are present at varying paths are not converged then minimized robustness conditions can be established with designed robot thereby minimizing total errors in the system. Further all underlying data can be distributed across certain distance where only reliable communication can be established. Figure 11 estimates the robustness of proposed and existing approach data can be distributed across certain distance where only reliable communication can be established.

Policy implications

The proposed work on robotic system for underwater monitoring system can be applied in industrial applications with the following benefits,

• The robotic procedure with fuzzy clustering algorithm can able to transmit the data at deep sea environments where hominids cannot able to collect such data.

• More number of fabricated sensors can be connected for all parametric measurements at subsurface areas and even less expensive robots can be implemented in monitoring systems.

Limitations and future work

The major limitations of proposed method are beyond certain depths the robotic underwater communication cannot be established or it is limited with varying cluster points (floating conditions). Hence, in future the proposed work can be extended without any clustering node points as cost of implementation is higher for each node points. Therefore instead of finding various cluster points and linking it to central server the node that best fits all points by the established robotic system can be identified thereby increasing the communication ranges. In addition the extended work can also be performed with minimized energy ranges even if density of considered underwater areas is much higher.