Fault location in a marine low speed two stroke diesel engine using the characteristic curves method

1.   Introduction

Due to the advantages of fuel economy and reliability, diesel engines have attained a leading position in marine applications, and the large two-stroke engine is widely used as the main power plant of civil ships ^[1,2].

To meet the requirements of Ocean transportation, Marine diesel engine has been developing towards the direction of intelligence and high efficiency ^[3,4], which also increases the complexity of diesel engine structure. This change increases the possibility of Marine diesel engine system failure. When a failure occurs in a marine main engine system, it will not only produce economic losses but also risk personnel safety

In the past decades, the maintenance of marine diesel engines has evolved from corrective actions to current trends. A lot of studies focus on predictive measures ^[5] that may improve the reliability of these engines. The purpose of these diagnostic systems is to detect and diagnose diesel engine anomalies before the anomalies cause undesired consequences.

A suitable diagnostic system requires a complete and reliable database that helps identify and diagnose anomalies when symptoms characterizing the abnormality are activated. In order to build a complete and reliable database, diesel engine simulation models have been used to reproduce the fault phenomena ^[6,7,8]. With the development of technology, real-time monitoring parameters are becoming more and more comprehensive ^[9].

In the available historical data on diesel engines, there are usually few historical records of typical faults. Introducing faults in real diesel engines cost a lot of time and fuel, and may compromise the safety of operators and engines ^[10]. Therefore, it is necessary to build thermodynamic models that act as simulators of the engine to collect faults data ^[11,12,13]. The AVLBoost©v2016 software is widely used by the scientific community to construct a one-dimensional wave action model ^[14,15,16] by collecting diesel engine geometry and operating data. The validation procedure is then performed by comparing the simulated and experimental values of the main operating parameters, which are obtained either by direct testing or by the manufacturer. On this basis, the virtual platform is constructed to collect the data of the engine under various operating conditions, especially in the case of failure.

A marine diesel engine has a complex structure. When a diesel engine breakdowns, a fault may unstably lead to various symptoms and a detected symptom may be caused by many different faults, which brings considerable difficulties to locate the real root causes of the diesel engine.

In recent years, machine learning and artificial intelligence technology have been widely used in the field of diesel engine fault diagnosis, which provides an effective tool to study the relationship between diesel engine faults and abnormal symptoms ^[17,18]. The deep learning method can use small data to develop fault diagnosis systems ^[19,20].

The fault tree method is an effective method to analyze the causal relationship between diesel engine faults and abnormal symptoms, where the diagnosis principle of this method is based on the expert's knowledge of the abnormalities ^[21,22].

The Marine diesel engine system needs to work in wet, vibratory and other harsh conditions for a long time, which leads to various faults of the Marine diesel engine system during operation. In extreme cases, multiple faults may occur at the same time. When multiple faults occur simultaneously in several different components, the coupling phenomenon between faults will affect the relationship between diesel engine faults and abnormal symptoms.

Therefore, there is a technical problem in the research field of diesel engine fault diagnosis to solve the problem of multi-fault diagnosis ^[23,24].

With the development of fault diagnosis based on the structural theory of thermoeconomics ^[25], the useful concepts of "intrinsic" and "induced" malfunctions have emerged ^[26,27], which may help better understand the causes and effects of failures. Compared with the theory of perturbations ^[28], the fault diagnosis method based on the thermoeconomic structure theory can obtain more accurate fuel impact values. Valero et al. ^[29] applied this method to the fault diagnosis of a 160MW coal-fired power plant and analyzed the influence of each component on the fuel consumption of the system. The authors used thermodynamic steady-state simulations to analyze the induced effects (induced malfunction and dysfunction) on other components caused by the intrinsic malfunction of a certain component, and they found that the highest additional fuel plant consumption was attributable to the component where the highest inefficiency occurs.

Verda et al. ^[30,31,32] studied the influence of the control system on thermoeconomic diagnosis using simulations to establish the corresponding "free condition" for different operating conditions. This "free condition" was mathematically determined using a specific model of the system. This particular condition is characterized by the same position of the governing parameters as that of the reference condition, but contains the anomalies occurring in the actual operating condition. On this basis, the influence of extra fuel consumption and irreversiblele losses caused by control system intervention is studied. It has been found that the control system intervention may generate higher induced malfunction in some components.

With the deepening of thermal-economic fault diagnosis, researchers ^[33] found that the complex interaction between components and the intervention of the control system may be the origin of induced malfunctions. These malfunctions are not actual faults within the corresponding components, but they appear because of the mutual interaction between the components' behavior. Thus, the reliability of this fault diagnosis technique may be strongly compromised if the induced malfunction cannot be identified and separated. However, the identification and separation of induced malfunctions are not easy.

Lazzaretto and Stoppato et al. ^[34] applied this method to the fault diagnosis of multiple complex energy systems to verify the reliability of the method. They found that when the degree of interaction between components in the system is low, this method is effectively able to locate the fault. On the other hand, when the system configuration is complex, this method cannot strictly guarantee the identification of the true source of the fault. The main reason is that it cannot isolate the propagation phenomenon of anomalies, and in turn cannot effectively identify the intrinsic malfunction and induced malfunction, because the variation of an operation parameter generated by the malfunction affects the exergy variables of both the components in which the malfunction occurs and those that suffer an induced malfunction.

On this basis, Toffolo and Lazzaretto et al ^[35] proposed a new method, named "Characteristic curve method" ^[36], to detect the malfunctions, based on the idea that the intrinsic malfunction of a component results in a change of its characteristic curve. Therefore, they proposed a new index to check whether the actual operating point of the component moves away from its reference operating condition along the characteristic curve or outside of it. Thus, it can be judged whether the anomaly of the component operation is due to anomalies in other system components (induced malfunctions) or to anomalies within the component (intrinsic malfunction).

In this paper, we propose a diagnosis method based on the characteristic curve of each component for isolating the propagation phenomena of faults in the system. The goal of this method is to realize the fault location of the diesel engine system When multiple faults occur simultaneously in several different components.

This paper describes the path and mode of fault propagation in the system. Then, based on the characteristics of each component in the diesel engine system, an accurate model of a marine diesel engine system is built after the selection of a suitable set of thermal performance parameters for the accurate description of the characteristic curve of each engine component. The method proposed in this paper is then verified by eight case studies for identifying the failure in the marine diesel engine system.

2.   Model

2.1.   The engine simulation model

The simulation model of the MAN 6S50 MC-C8.1 Diesel engine was established with AVLBoost©v2020. The specification of the engine are shown in Table 1.

According to the manufacturer specifications, the diesel fuel used in the engine certification tests is Marine Gas Oil.

The model simulates the indicated cycle. The gas composition and thermodynamic properties in each element of the intake and exhaust systems piping discretization at any simulation time step (i.e., crank angle) are calculated by solving the one-dimensional conservation equation set commonly used in engine one-dimensional gas-dynamic simulations ^[37], i.e., mass Eq (1), momentum Eq (2) and energy Eq (3) conservation Eq (4) coupled with the ideal-gas constitutive equation, which writes:

The average cell size is set to 100 (Target Average Cell Size for Spatial Pipe Discretization), and the convergence control is set in several components. The simulation calculation finishes when at least three engine cycles meet the convergence criteria. The convergence criterion is that the variation of the cycle averaged values ("transients") of the IMEP of each cylinder in BOOST™ elements over the last three consecutive cycles is less than a prescribed threshold (500 Pa). In addition, the fuel used in the test bench has the same chemical composition as the vessel.

The components of the model are shown in Figure 1. The system consists of the following components connected by pipes: air filter, compressor, air cooler, intake manifold, cylinders, exhaust manifold and turbine. In the simulation model, measuring points are located in the most relevant positions.

The components that make up the model are connected by unidimensional pipes. The pipe parameters include length, equivalent diameter, friction coefficientand wall temperature. The local pressure drop of the air filter is set to a fixed value in the range of 0~0.02 bar. The type of turbocharger is TCA66-21. The complete turbine and compressor maps are input into the marine diesel engine model through tools provided by the software to make sure that the turbocharging process can respond to the actual situation when the boundary conditions change or failure conditions are introduced in the model. The cooling capacity of the air cooler is determined by the inlet temperature of the cooling water and the efficiency of the air cooler. The simulation model considers the actual volume of intake and exhaust manifolds. The heat transfer coefficient of both intake and exhaust manifold models is 0.

Cylinders are defined in terms of their design dimensions, geometric compression ratio, combustion, heat transfer and scavenging port and exhaust valve data. The heat release rate of the combustion process is simulated by a Wiebe law ^{[38,39,40,41]}. Blow-by is not considered in this article. The lift curve of the scavenging port and exhaust valve is used to determine the filling and emptying of a cylinder. The Woschni 1990 heat transfer model is used to simulate convective heat losses.

2.2.   Model validation

The model was verified by comparing the simulation data with the engine shop test data. Table 2 shows the comparison between the mean values of the simulation and experimental main parameters ^[42]. The deviation between simulation and experimental values is generally less than 5%. In addition, the verification of the relationship Speed-Power, Speed-SFOC, Speed-Boost Pressure and Speed-Turbocharger Outlet Temperature was also performed, as shown in Figures 2−5.

Therefore, it is considered that the model has good accuracy in simulating engine behavior, and can be used as an abnormal simulation platform without the need to generate failures in a real engine and with a consequent remarkable saving of fuel and time.

3.   Fault location method

3.1.   Propagation phenomenon of failure

The mass and energy flow of the diesel engine system is shown in Figure 6. When a component of the system has a failure, the thermodynamic quantities of the mass and energy flow associated with the abnormal component are therefore altered. Due to the interaction among components, this modification affects the operations of other components in turn. Therefore, the impact of the anomaly will propagate through the system, affecting the performance of all relevant components in the system.

For better and easy understanding, the compressor failure (5% reduction in compressor isentropic efficiency) case is taken as an example. As shown in Figure 7, in the case of a compressor failure, the performance of other components in the system where the anomaly does not exist also changed. This phenomenon occurs because compressor failure changes the operating conditions of other components ^[36,43]. The failure of the compressor will change the mass flow, pressure and temperature of the air at the outlet of the compressor, resulting in changes in the operating conditions of the air cooler. Although there is no fouling or blockage in the air cooler, the operating state of the air cooler will change accordingly. Based on similar principles, the working performance of components such as cylinders and turbines will also change.

In other words, due to the interaction among components, the changes caused by the intrinsic malfunction can spread throughout the system, creating induced malfunction in the components where the anomaly does not exist. This phenomenon of fault propagation in the system can interfere with fault localization.

3.2.   Definition of characteristic curve and diagnostic index

The failure or anomaly of a component (such as changes in the compressor blade geometry, blockage of an air cooler, deposits on heat exchange surfaces, etc.) will affect the functional relationships among the thermodynamic variables (temperature, pressure, mass flow rates, etc.) on which the mass and energy streams involved in the operation of that component depend. These functional relationships are often referred to as component characteristic curves (performance maps in machines, heat transfer models for heat exchangers).

As shown in Figure 8, the operating state of the component will deviate from its original reference state characteristic curve (broken line) and move from the reference state (point A) to a new state (point C). Due to the interaction among components, the alterations caused by the failure of the component will spread through the whole system, affecting the operating states of other components, which react to the changes imposed by the faults in another component according to their non-modified characteristic curves. As shown in Figure 8, the operating state of a component in perfect order will not deviate from the original characteristic curve and move from the reference state (point A) to a new state (point B). In other words, external factors or induced factors do not affect the characteristic curve of the component that can be affected only by internal factors. External, induced and internal factors are defined as follows ^[33]: External factors-modification of external conditions such as environment variables. Induced factors-variations caused by the change of other system variables, e.g., component interaction or the intervention of the control system. Internal factors-degradation or failures.

The location of malfunctioning components depends on the knowledge of the characteristic curve of each component in mathematical form. In particular, Eq (5) formalizes the characteristic curve of the component ith by a set of relationships f that define a performance parameter or a thermodynamic variable π characterizing the component behavior as a function of a subset $\delta_k$ of the independent variables involved in the component operation.

On the other hand, it is always possible to quantify with ${\pi }^{i, real}$ the actual value of the performance parameter ${\pi }^{i}$ when the component operates at a specific real condition, and with ${{\bf{I}}}_{{{index}}}^{{{i}}}$ the difference between ${\pi }^{i, real}$ and the value of the performance parameter ${\pi }^{i}$ as expected from Eq (5) for the corresponding operating condition. The difference ${{\bf{I}}}_{{{index}}}^{{{i}}}$ writes as reported in Eq (6).

Therefore, during the real operation of the component under normal behavior of the system that embeds the component, the result of Eq (6) is zero, since the working point of the component ith, corresponds to the operating condition predicted in accordance with the reference characteristic curve. In contrast, when a performance degradation or fault changes the characteristic curve of the component, the result of Eq (6) will be different from zero. Thus, ${{\bf{I}}}_{{{index}}}^{{{i}}}$ can be used as a diagnostic index.

The characteristic curve of the component can be linearly approximated by using its derivative as calculated in the reference state (as shown in Figure 8, the tangent AB₁ in the reference state, approximates the point B with the point B_1, the slope of the tangent AB₁ is the derivative $\partial f^{i, r e f} / \partial \delta_k^i$, at point A, the quantity $\epsilon$ stands for the "residual effects"). In mathematical terms, such approximation can be formalized as reported in Eq (7).

Combining Eq (5) to Eq (7), ${{\bf{I}}}_{{{index}}}^{{{i}}}$ can be formulated as

As shown in Figure 9, if the real operating point of the component is on the original characteristic curve, moving from reference state A to the new state B, the malfunction of the component is only an induced effect. In this case, neglecting the approximation introduced by the linearization of the characteristic curve, ${{\bf{I}}}_{{{index}}}^{{{i}}}$ = 0. In contrast, if the component has an intrinsic malfunction, the real operating point of the component will depart from the characteristic curve, moving from reference state A to the new state C, and the value of ${{\bf{I}}}_{{{index}}}^{{{i}}}$ is expected to be non-zero.

3.3.   The choice of variable π

The main components in the diesel engine system can be divided into two categories. The first category includes all the "work components", i.e., the components whose product can be expressed as useful exergy. For example, the turbocharger compressor consumes the mechanical work provided by the turbine to increase the internal energy of the air. The second category includes all the "dissipative components", whose product cannot be expressed as useful exergy. For example, the air coolers dissipate heat and reduce the temperature of the cylinder intake air, and the dissipated internal energy is the target product of the air cooler.

In this paper, the irreversibility is selected as parameter π for the diagnostic index ${{\bf{I}}}_{{{index}}}^{{{i}}}$ of the components embedded into the diesel engine system. This because:

The irreversibility Iⁱ includes the knowledge related to the mass and energy flows and directly reflects the efficiency of the energy conversion process.

For the "work component", the existence of anomalies will always increase the diagnostic index ${{\bf{I}}}_{{index}}^{i}$.

For the "dissipative component", the existence of anomalies will always reduce the diagnostic index ${{\bf{I}}}_{{index}}^{i}$.

In summary, if the component has an intrinsic malfunction (degradation or failure of the component), the indicator ${{\bf{I}}}_{{index}}^{i}$ of the component will change.

3.4.   The characteristic parameters of component

The basic rule for the selection of variables ${{{\delta}}}_{{{k}}}^{i}$ is that they must be a set of independent variables characterizing the behavior of the component. Therefore, the component characteristic curves ${{{f}}}^{{{i, ref}}}$, and so the derivatives ${{\partial}}{{{f}}}^{{{i, ref}}}/{{\partial}}{{{\delta}}}_{{{k}}}^{i}$, can be defined as functions of ${{{\delta}}}_{{{k}}}^{i}$ ^[36].

For an energy system, all performance variables can be expressed as a function of thermodynamic variables, so thermodynamic variables are the actual independent variables of the energy system.

In addition, exergy represents a synthesis of thermodynamic information that is useful in describing the outcomes of component behavior.

As shown in Section 3.2 of this article, a component's performance is determined by its own physical constraints (characteristic curves) and operational parameters.

Therefore, the natural choice for these variables is a set of independent component thermodynamic variables (including mass flow, pressure and temperature). The number of independent variables is equal to the number of component degrees of freedom.

However, for components with complex production structures or energy conversion, such as cylinders of diesel engines, the required number of independent variables available cannot be monitored. Therefore, specific output parameters should be used to replace the available arguments that cannot be monitored.

As shown in Figure 6, exergy flowing into the compressor includes air exergy flow at compressor inlet E_xa1 and mechanical exergy W_C.

Therefore, the independent variable group representing the compressor characteristic curve includes m_xa1, T_xa1, P_xa1, n_C and T_C.

However, the signal monitoring of compressor speed and torque is difficult and costly. The relationship between compressor outlet thermal parameters and W_C is shown in Eqs (12)–(15).

So, the independent variable group representing the compressor characteristic curve includes m_xa1, T_xa1, P_xa1, T_xa2 and P_xa2.

The selection principle of the independent variable group of the air cooler is similar to the superheater ^[44]. Considering that the flow rate and pressure of the cooling water are constant. The independent variable group representing the air cooler characteristic curve includes m_xa2, T_xa2, P_xa2 and T_coolant.

For the diesel engine system, the function of the cylinder is to use part of the high-pressure air sent by the compressor to burn the fuel and to mix the combustion products with the rest of the high-pressure air to form high-temperature and high-pressure gas, which drove the piston to produce mechanical exergy as shown in Figure 6. Therefore, the performance of the cylinder is also related to its mechanical structure (design parameters).

Take cylinder No. 1 as an example.

E_xf1 indicates the chemical exergy of the fuel.

E_xa4 represents air exergy flow at the inlet.

E_xg1 indicates exhaust gas exergy flow.

Thermodynamic processes, chemical reactions, mechanical work, heat transfer, mass diffusion and friction processes occur simultaneously within this component. In other words, the irreversible losses in the working process of the cylinder must include irreversibility losses due to fuel combustion, cylinder heat transfer, exhaust gas, mechanical friction, etc. The description of each irreversibility loss requires monitoring a large number of characteristic parameters, such as compression end temperature, atomization of the fuel in the cylinder, etc., which are very demanding to be managed and some of the parameters are not easy to measure with the standard marine engine technology. On the other hand, the overall irreversibility loss in the cylinder can be calculated by the cylinder input energy and the cylinder output work.

The indicated mean effective pressure (IMEP) is the work output of one cycle for unit swept volume and relates to the cylinder power in accordance with Eq (19).

W_i——Power of the ith cylinder, [kW]

$n$——diesel engine speed, [r/min]

IMEP_i——Mean Effective Pressure of the ith cylinder, [kPa]

D——bore, [mm]

S——stroke, [mm]

Therefore, for the diesel engine system, the independent variable group representing the cylinder No. 1 characteristic curve includes m_xa4, T_xa4, P_xa4, and m_f1.

The selection principle of the independent variable group of the turbine is similar to the compressor. However, according to the differences between the compressor map and the turbine map, the independent variable group representing the turbine characteristic curve includes m_xa7, T_xa7, P_xa7 and P_xa8.

The characteristic parameters selected for the cylinder and all of the other engine components considered in this study are shown in Tables 3 to 6. It should be noted that the fuel quantity injected in each cylinder is assumed here as a constant value related to the diesel engine load because, in current diesel engine systems, it is difficult to monitor the flow rate in each fuel injector.

The measurement points setting in the simulation model are shown in Figure 10.

3.5.   The fault indicator

For "work components" the diagnostic index ${{\bf{I}}}_{{index}}^{i}$ can be expressed as in Eq (20).

For "dissipative components" the diagnostic index ${{\bf{I}}}_{{index}}^{i}$ can be expressed in Eq (21).

The ΔI^{i, calc} is the expected variation of component irreversibility due to a change Δ$\delta k$ of the component independent variables, according to the reference component characteristic curve.

Since the analytic form of each characteristic curve is generally unknown, the derivatives $\partial I^{i, r e f} / \partial \delta_k^i$ of every component can be calculated by generating several virtual operating conditions near the reference operation using a simulator.

In order to make the reference state close to the actual state, it is necessary to change the diesel engine speed and fuel injection quantity.

W_e——Nominal engine power, [kW]

n_e——Nominal engine speed, [r/min]

W——Diesel engine power, [kW]

$n$——Diesel engine speed, [r/min]

$\Delta h$——The amount of oil supplied to one cylinder in 100 engine cycles, [ml];

${g}_{e}$——Fuel consumption rate, [g/(kW·h)];

${{W}}$——Diesel engine power, [kW];

$\gamma$——Density of fuel oil, 0.825[g/(cm3)] for diesel;

L——Number of cylinders;

$n$——Diesel engine speed, [rpm].

In the reference state, Eq (22) allows calculating the speed of the diesel engine, whereas Eq (23) allows estimating the amount of fuel injected in the cylinder.

Taking the turbine as an example, four virtual operating conditions (ref1, ref2, ref3 and ref4) are required to calculate the derivatives of the turbine, since the number of component independent variables is four (P_MP10, T_MP10, P_MP11 and m_MP10). as shown in Eq (24). Note that the turbine outlet pressure is an environmental variable (atmospheric pressure). To avoid the rank of the equations being less than the number of independent variables of the equation, resulting in countless solutions to the equation, at least two different turbine outlet pressures should be set among the four reference states generated by the simulation simulator.

4.   Results and discussion

Once the model has been adjusted and validated, failures are introduced one by one.

The compressor failure F1 is usually caused by dust accumulation in the impeller or diffuser as well as damages that produce changes in geometry. The compressor failure is simulated by reducing the isentropic efficiency of the compressor.

The air cooler failure F2 is usually caused by the increase of fouling on the inner wall of the air cooler, which will produce a reduction of cooling capacity. The air cooler failure is simulated by reducing the isentropic efficiency.

This kind of cylinder failure F3 (Blocking of the injector hole of the cylinder) is usually caused by the fault of the fuel injection system or the carbon accumulation of the nozzle, resulting in a reduction in the corresponding fuel mass flow rate.

This kind of cylinder failure F4 (Excessive blow-by) is usually caused by abnormal wear of the piston ring, which is simulated by increasing the clearance between the piston ring and the sleeve.

The turbine failure F5 is usually caused by dust accumulation in the impeller or diffuser as well as damages that produce changes in geometry. The turbine failure is simulated by reducing the isentropic efficiency of the turbine.

In this paper, the method has been verified by cases real 1~8 as shown in Table 7.

Table 8 provides the details of cases real 1 to real 8.

Table 9 provides the details of the of the reference cases.

The diagnosis results of cases real 1–8 operating conditions are listed in Tables 10−17, in which each row referring to the malfunctioning components is highlighted in bold.

For example, looking at Table 10, first, it is worth noting that all the failures are accurately located and identified. In particular, the expected irreversibility variation of all components is higher than 0, which means that the propagation of the induced effects caused by failures involves all components in the system.

In addition, it can be found in Table 16 that all the failures are accurately located and identified. However, this method cannot identify the type of failure (piston ring abnormal wear or fuel pump wear).

Focusing on the malfunctioning components (i.e., the compressors and air coolers), the value of the index ${{\bf{I}}}_{{index}}^{i}$ (see the last but one column in the table) is high. This means that the actual irreversibility of such components is noticeably different from the expected irreversibility, indicating that their characteristic curve has changed because of their intrinsic operation anomalies. In contrast, the corresponding values of index ${{\bf{I}}}_{{index}}^{i}$ for the other components are close to 0 (note that the non-zero value is mostly due to the error ε in the approximation of the derivative), which means that the actual irreversibility of these components is basically equal to the expected irreversibility, i.e., the components are affected by malfunction induced effects and their characteristic curves do not deviate from the original one.

Finally, since the exergy flow rate of different components of the diesel engine system varies greatly, the ratios ${{\bf{I}}}_{{index}}^{i}$/|ΔI^{i, calc}| that are reported in the last column of the table, are the more proper diagnostic indexes to take into consideration. Tables 9 to 16 show that this index amplifies the anomaly of the components in which the intrinsic malfunction occurs increasing the gap existing between these components and the others, which are affected only by the approximation error in the evaluation of the derivatives of the characteristic curves. Thus, this index greatly simplifies the failure location and identification process.

5.   Conclusions

This paper proposes a diagnosis method for diesel engines based on the characteristic curve of each component. When multiple faults occur simultaneously in several different components, the advantage of this method is to effectively locate the malfunctions, so as to maintain the reliability of the system. The author establishes and verifies the reliable model of the 6S50 engine and each of its components, and then describes the characteristic curve of each component. On this basis, eight multiple malfunctions cases have been diagnosed and discussed to show the ability of the proposed method.

The following conclusions can be drawn from this application:

1) The validity and reliability of the method were demonstrated by eight test cases. The method is able to effectively isolate the propagation phenomena of faults in the system, and accurately identify the location of faults in the marine diesel engine system.

2) The author selected comprehensive and practical thermal performance parameters (that can be monitored) to describe the characteristic curves of the main components (compressor, turbine, cylinder and air cooler). Therefore, the proposed fault location method has high practical application value.

3) Both the irreversibility in the i^th component, ${{\bf{I}}}_{{index}}^{i}$ and ${{\bf{I}}}_{{index}}^{i}$/|ΔI^{i, calc}| and can be used as fault location indicators for the marine diesel engine system. Considering the exergy flow rate of different components of diesel engine systems varies greatly, it is more effective to choose ${{\bf{I}}}_{{index}}^{i}$/|ΔI^{i, calc}| as the fault location indicator.

4) The fault diagnosis method proposed in this paper can effectively locate malfunctions, but this method cannot identify the type of failure (piston ring abnormal wear or fuel pump wear). This method still needs to be combined with other fault identification methods to identify the type of failure.

Conflict of interest

The authors declare there is no conflict of interest.