Application of Binary Particle Swarm Optimization ... - Semantic Scholar

Application of Binary Particle Swarm Optimization in Cryptanalysis of DES Shimpi Singh Jadon, Harish Sharma, Etesh Kumar, and Jagdish Chand Bansal ABV-Indian Institute of Information Technology and Management, Gwalior {shimpisingh2k6,eteshkumar,jcbansal}@gmail.com, [email protected]

Abstract. Feistel cipher based cryptographic algorithms like DES are very hard for the cryptanalysts as their internal structures are based on high nonlinearity and low autocorrelation. It has been shown that the traditional and brute-force type attacks are insignificant for the cryptanalysis of this type of algorithms. Swarm intelligence is an exciting new research field and shown their effectiveness, robustness to solve a wide variety of complex problems. Therefore, in this paper, Binary Particle Swarm Optimization (BPSO) strategy is used for cryptanalysis of DES symmetric key cryptographic algorithm. The reported results show that it is very promising to solve block cipher based cryptographic optimization problem through meta heuristic techniques. Keywords: Meta Heuristics, Particle swarm optimization, Data Encryption Standard, Cryptanalysis, Evolutionary computation.

1 Introduction Swarm Intelligence is a meta-heuristic method in the field of artificial intelligence that is used to solve optimization problems. It is based on the collective behavior of social insects, flocks of birds, or schools of fish. However, a swarm can be considered as any collection of interacting agents or individuals. These animals can solve complex tasks without centralized control. Researchers have analyzed such behaviors and designed algorithms that can be used to solve combinatorial and numerical optimization problems in many science and engineering domains. Previous research [16, 8, 12] has shown that algorithms based on Swarm Intelligence have great potential. The algorithms that have emerged in recent years include Ant Colony Optimization (ACO) [16] based on the foraging behavior of ants, and Particle Swarm Optimization (PSO) [8] based on the behaviors of bird flocks and fish schools. Particle Swarm Optimization is one of the stochastic optimization technique and in this paper it is used for cryptanalysis of a feistel cipher based algorithm. The main reason for using PSO here is its global solution finding K. Deep et al. (Eds.): Proceedings of the International Conference on SocProS 2011, AISC 130, pp. 1061–1071. c Springer India 2012 springerlink.com

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property, without any need to give initial approximation to unknown parameters. Particle Swarm optimization (PSO) technique is considered as one of the modern heuristic algorithms for optimization introduced by James Kennedy and Eberhart in 1995 [8]. It is based on the social behavior metaphor [8]. It is a population based optimization technique, which is sometimes regarded as an alternative tool to Genetic Algorithm (GAs) and other Evolutionary Algorithms (EAs) and gained a lot of attention in the recent years. As compared to EAs, PSO is a stochastic search technique with reduced memory requirement, computationally effective and easier to implement. Also PSO has a more global searching ability at the beginning of the run and has greater local search ability near the end of the run [1]. Cryptanalysis is the study of methods for obtaining the meaning of encrypted information. The aim of this paper is to use PSO and its variant Binary PSO for cryptanalysis of Feistel-cipher based cryptosystems. More specifically, in this paper, Binary PSO is applied for finding some missing bits of the key of data encryption standard (DES) symmetric key cryptographic algorithm for four rounds. Furthermore, a comparative study also carried out for Binary PSO and PSO in terms of efficiency and accuracy. The rest of the paper is organized as follows: In Section 2, PSO algorithm is briefly described. In section 3, DES cryptosystem and differential cryptanalysis are briefly reviewed and the optimization problem is formulated. The experimental results are reported in section 4. Finally, in section 5, conclusions are derived and directions for future work are suggested.

2 Brief Overview of Particle Swarm Optimization The field of nature-inspired metaheuristics is mostly constituted by the evolutionary algorithms [comprising of GAs, EP, ESs, differential evolution (DE), and so on] as well as the swarm intelligence algorithms [e.g., ant colony optimization (ACO) [6], particle swarm optimization (PSO) [8] and bacterial foraging optimization (BFO) [11]]. From the aforementioned algorithms, in this paper, Binary version of PSO is used for cryptanalysis of four-rounded DES. Particle Swarm optimization (PSO) technique is considered as one of the modern heuristic algorithms for optimization introduced by James Kennedy and Eberhart in 1995 [8]. The idea behind PSO is based on the simulation of the social behavior of bird flock and fish schools. PSO is a swarm intelligence method for global optimization problems. It differs from wellknown evolutionary algorithms as in evolutionary algorithms a population of potential solutions is used to probe the search space, but no operators, inspired by evolution procedures, are applied on the population to generate new promising solutions. Instead in PSO, each individual, namely particle, of the population, called swarm, adjusts its trajectory towards its own previous best position (pbest), and towards the previous best position of any member of its topological neighborhood (gbest). Two variants of the PSO have been

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developed, one with a global neighborhood and the other with a local neighborhood. According to the global variant, each particle moves towards its best previous position and towards the best particle in the whole swarm. On the other hand, in the local variant, each particle moves towards its best previous position and towards the best particle in its restricted neighborhood. Working of PSO may be briefly described as under: Suppose the search space is D-dimensional, then the ith particle of the swarm can be represented by a D-dimensional vector, Xi = (xi1 , xi2 , ..., xiD )T . The velocity (position change) of this particle can be represented by another D-dimensional vector Vi = (vi1 , vi2 , ..., viD )T . The best previously visited position of the ith particle is denoted as Pi = (pi1 , pi2 , ..., piD )T . Defining g as the index of the best particle in the swarm, the swarm is manipulated according to the following two equations: Velocity Update Equation: vid = vid + c1 r1 (pid − xid ) + c2 r2 (pgd − xid )

(1)

Position Update Equation: xid = xid + vid

(2)

where d = 1, 2, ..., D; i = 1, 2, ..., S, where S is the size of the swarm; c1 and c2 are constants, called cognitive and social scaling parameters respectively (usually, c1 = c2 ; r1 , r2 are random numbers, uniformly distributed in [0, 1]). Equations (1) and (2) define the initial version of PSO algorithm. A constant, V max, was used to arbitrarily limit the velocities of the particles and improve the resolution of the search. The pseudo code of PSO is shown below: Algorithm PSO: for t= 1 to the max. bound of the number on iterations do for i=1 to the swarm size do for d=1 to the problem dimensionality do Apply the velocity update equation: Update Position end for Compute fitness of updated position; if Needed then update historical information for Pi and Pg ; end if end for Terminate if Pg meets problem requirements; end for The maximum velocity V max, serve as a constraint to control the global exploration ability of particle swarm. A larger V max facilitates global exploration, while a smaller V max encourages local exploitation. The concept of an

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inertia weight was also developed to better control exploration and exploitation. The motivation was to be able to eliminate the need for V max. The inclusion of an inertia weight in the particle swarm optimization algorithm was first reported in the literature in 1998 [13, 14]. After some experience with the inertia weight, it was found that although the maximum velocity factor, V max, could not always be eliminate, the particle swarm algorithm works well if V max set to the value of the dynamic range of each variable (on each dimension). The resulting velocity update equation becomes: vid = w × vid + c1 r1 (pid − xid ) + c2 r2 (pgd − xid )

(3)

Eberhart and Shi [7] indicate that the optimal strategy is to initially set w to 0.9 and reduce it linearly to 0.4, allowing initial exploration followed by acceleration toward an improved global optimum. Maurice Clerc [3] has introduced a constriction factor, χ , which improves PSO’s ability to constrain and control velocities. χ is computed as: χ=

|2 − φ −

2 φ(φ − 4)|

(4)

where φ = c1 + c2 , φ > 4, and the velocity update equation is then vid = χ × (vid + c1 r1 (pid − xid ) + c2 r2 (pgd − xid ))

(5)

Eberhart and Shi [7] found that χ , combined with constraints on V max, significantly improved the PSO performance. Discrete binary version of PSO was proposed by Kennedy and Eberhart for binary problems [9]. In their model a particle will decide on ”yes” or ” no”, ”include” or ”not to include” etc. These binary values can be a representation of a real value in binary search space. Same, as in continuous version, the particle’s personal best and global best is updated in binary PSO. The major difference between binary and continuous version of PSO is that in binary PSO, velocities of the particles are rather defined in terms of probabilities that a bit will change to one. According to above definition a velocity must be within the range [0,1]. So a sigmoid function defined as (sig(v) = (1 + e−vid )−1 ) is used to map all real valued numbers of velocity to the range [0,1] [9]. Also to update the velocity vector of the particle, equation (3) is used. The equation (6) is used for obtaining the new position of the particle. 1 if U (0, 1) < sig(vij (t + 1)) xij (t + 1) = (6) 0 otherwise. Where U(0,1) is the uniform random number.


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3 DES as an Optimization Problem 3.1 Data Encryption Standard The data encryption standard (DES) is basically a Feistel iterated block cipher. For DES, data are encrypted in 64-bit blocks using a 56- bit key. The algorithm transforms 64-bit input in a series of steps into a 64-bit output.To reverse the encryption same steps, with the same key are used but in reverse order. Input to the DES cipher is plaintext P and output is ciphertext C, with each block 64 bits. Through a 16-round process, the current 64-bit word is divided into two parts 32-bit each, the left part Li and the right part Ri . Then round i, 1 ≤ i ≤ 16 is defined as follows Li = Ri−1 , Ri = Li−1 ⊕ F (Ri−1 , Ki ), Where Ki is derived from the cipher key K via the key scheduling algorithm, Ki is the 48 bits subkey used in ith round, and F is a round function. The round function F is the main component of DES. Mainly three operations are involved in round function i.e substitution, permutation and XOR operations (denoted by ⊕). The S-boxes are the only nonlinear part of DES and basically S-boxes are nonlinear mapping. There are eight S-boxes each of which is a substitution mapping 6 to 4 bits. Detailed description of DES is given in [5]. Differential cryptanalysis is a chosen plaintext attack meaning that the attacker must be able to obtain encrypted ciphertexts for some set of plaintexts of his choosing. The two plaintexts can randomly be chosen, as long as they satisfy the difference condition. In this method the effect of particular differences in plaintext pairs on the differences of the resultant ciphertext pairs is analysed. Using these differences, probabilities can be assigned to the possible keys and locate the most probable key. The difference is chosen as a fixed XORed value of the two plaintexts for cryptosystems similar to DES. Characteristic is the most important component in differential cryptanalysis. The definition of a characteristic is the following. ”Associated with any pair of encryptions are the XOR value of its two plaintexts, the XOR of its ciphertexts, the XORs of the input of each round in the two executions and the XORs of the outputs of each round in the two executions. These XOR values form an r-round characteristic . A characteristic has a probability, which is the probability that a random pair with the chosen plaintext XOR has the round and ciphertext XORs specified in the characteristic” [2].

3.2 Formulation of the Problem Biham and Shamir [2] use a one-round characteristic with probability 1 for the differential cryptanalysis of DES reduced to four rounds, and at the first step differential cryptanalysis provides 42 bits of the subkey of the last round. Subkeys are calculated using the DES key scheduling algorithm, differential

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cryptanalysis gives 42-bit which are actual key bits of the 56 key bits and still there are 14 key bits missing. One of the method for finding these key bits was to try all the 214 possibilities in decrypting the given ciphertexts, using the resulting keys. Known plaintext XOR value for all the pairs that are used by differential cryptanalysis should be satisfied with the right key. The probability for remaining 214 − 1 values of the key will be only 2−64 to satisfy the pairs condition [2]. We formulate the problem of finding the missing 14 bits to an optimization one, as follows. each one of the 14 bits is considered as a component of a 14th dimensional vector. This vector represents a possible solution of the problem. Now, assume that the right 42 key bits which were obtained by differential cryptanalysis were suggested using np pairs. These np pairs can be used to evaluate the possible solutions provided by the optimization method.For each possible solution, Xi , obtained by the optimization algorithm, we construct the 56 bits of the key comprising 42 bits which are known by differential cryptanalysis and the 14 components of Xi in proper order. All np ciphertext pairs that were used by differential cryptanalysis decrypted with the resulting key and number of decrypted pairs that satisfy the known plaintext XOR value is counted, denoted as cnpXi . Thus, the evaluation function f, is the bitwise difference between the desired output np and the actual output cnpXi given by [10]: f (Xi ) = np − cnpXi (7) For the above function f, zero is the global minimum and actual key will be the global minimizer with probability P = 1 − 2−64 .

4 Experimental Results and Discussion The PSO and BPSO methods, are applied on the considered problem with two different examples. Subsequent subsections contain the experimental settings and results with proper statistical analysis using Performance indices [4] and boxplots [15].

4.1 Experimental Settings The experimental settings of various parameters for BPSO and PSO, are shown as follows. This is the most recommended parameter setting. 1. 2. 3. 4. 5.

Iterations/Generations=Swarm × 10, Total Runs=100, Acceleration constants (c1 , c2 )=(2.05,2.05), Inertia Weigh= Linearly decreasing from (0.8 to 0.1), Maximum Velocity (Vmax )=2.


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4.2 Experimental Results In order to compare the performance of Binary PSO (BPSO) and PSO, two examples are taken into consideration (Listed in Table 1.1 and Table 1.2). In example-1, 5 test pairs and in example-2, 10 test pairs are considered for finding the missing 14 key bits. Numerical results obtained by BPSO and PSO are tabulated in Table 1.1 and Table 1.2. In Table 1.1 and 1.2, success rate (SR) and average function evaluations (AF E) are shown for both the algorithms. Table 1. Comparison of the Methods for 5 Test Pairs Key k1 k2 k3 k4 k5 k6

PSO SR AFE 100 2815 97 2516 98 2704 100 2393 98 2861 99 2414

Binary PSO SR AFE 100 1540 99 1598 100 1645 100 1324 100 1554 100 1462

Table 2. Comparison of the Methods for 10 Test Pairs Key k1 k2 k3 k4 k5 k6

PSO SR AFE 100 2613 99 2105 100 2463 100 2198 98 2487 100 2253

Binary PSO SR AFE 100 1465 100 1286 100 1436 100 1232 100 1327 100 1121

4.3 Statistical Analysis In order to extract the best strategy for finding the missing 14 key bits, a comparative analysis is done for P SO and BP SO. Statistical comparison is carried out using performance index [4] and boxplot. In order to compare the consolidated performance of BP SO and P SO search heuristics, the value of a performance index P I [4] is computed. This index gives a weighted importance to the success rate and the average number of function evaluations. The value of this performance index for a computational algorithm under comparison is given by Np 1 (k1 αi1 + k2 αi2 ) PI = Np i=1

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Where • • •

αi1

=

Sr i T ri ;

αi2

=

Mf i Af i ,

0,

if Sri > 0. ; if Sri = 0.

Sri = Number of successful runs of ith problem T ri = Total number of runs of ith problem M f i = Minimum of average number of function evaluations of successful runs used by all algorithms in obtaining the solution of ith problem Af i = Average number of function evaluations of successful runs used by an algorithm in obtaining the solution of ith problem Np = Total number of problems analyzed.

• •

k1 and k2 (k1 +k2 = 1 and k1 , k2 ≤ 1) are the weights assigned to success rate and average number of function evaluations of successful runs respectively. From above definition it is clear that P I is a function of k1 and k2 . Since k1 + k2 = 1, one of ki , i = 1, 2 could be eliminated to reduce the number of dependent variables from the expression of P I. We adopt the same methodology as given in [4] i.e. equal weights are assigned to two terms at a time in the P I expression. This way P I becomes a function of one variable. The resultant cases are as follows: 1−W 2 1−W 2

1. k1 = W, k2 = 2. k2 = W, k1 =

, 0 ≤ W ≤ 1; , 0 ≤ W ≤ 1;

For example-1 (Table 1.1), graphs for cases (1) and (2) are shown in Fig. 1.1(a) and 1.1(b) respectively and for example-2 (Table 1.2), graphs for cases (1) and (2) are shown in Fig. 1.2(a) and 1.2(b) respectively. In these figures the horizontal axis represents the weight W and the vertical axis represents the performance index P I. P Is of both algorithms (P SO, BP SO) are superimposed in the Figures 1.1 and 1.2 for comparison and to get a ranked order of the performance. It is observed that for BP SO, the value of PI is more than P SO. It is concluded from P I that BP SO is proved to be the a better choice compared to PSO to solve these type of optimization problems. 1.5

Performance Index

Performance Index

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PSO BPSO 0 0

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0 0

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Weight (k1)

Weight (k2)

(a)

(b)

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Fig. 1. Performance index analysis for e.g. 1; (a) for case (1) and (b) for case (2)

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Fig. 2. Performance index analysis for e.g. 2; (a) for case (1) and (b) for case (2)

For the purpose of comparison in terms of performance, boxplot analysis is carried out for both the algorithms. The empirical distribution of data is efficiently represented graphically by the boxplot analysis tool [15]. Analysis of univariate expression, where the variability of measurements may be affected by many parameters is effectively done by the boxplot tool. Degree of dispersion and skewness in the data are easily analyzed by measuring the spacings between the different parts of the box. The boxplot based on average function evaluation for example-1 and example-2 for both the algorithms are shown in Fig. 1.3-1.4. For example-1, it is clear from Fig. 1.3 that the performance of BPSO is better than PSO. For example-2, it is observed from Fig. 1.4 that BPSO performs better than PSO.

Average Function Evaluation

2800 2600 2400 2200 2000 1800 1600 1400 PSO

Strategy

BPSO

Fig. 3. Boxplot graph of average function evaluation for example 1

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Fig. 4. Boxplot graph of average function evaluation for example-2

5 Conclusion In this paper, Binary Particle Swarm Optimization (BPSO) method is analyzed for the cryptanalysis of DES block ciphers. Differential cryptanalysis can locate 42 actual key bits of the 56 key bits of DES and then BPSO is applied for finding 14 missing key bits. Since its inception, PSO has gained wide popularity due to its ability to solve complex optimization problems in a very efficient and simple manner. The results produced in this paper show that the use of BPSO is a better choice for the cryptanalysis of feistel cipher based cryptographic algorithms. A comparative analysis of BPSO and PSO also carried out. In future, it will be very interesting to see the use of evolutionary algorithms for cryptanalysis of these type of optimization problems with higher intensity. Acknowledgement. First, second and third Author acknowledge ABV- Indian Institute of Information Technology and Management Gwalior for providing research grant under MHRD scheme to carry out this work.

References [1] Arumugam, M.S., Rao, M.V.C., Tan, A.W.C.: A novel and effective particle swarm optimization like algorithm with extrapolation technique. Applied Soft Computing 9(1), 308–320 (2009) [2] Biham, E., Shamir, A.: Differential cryptanalysis of des-like cryptosystems. Journal of CRYPTOLOGY 4(1), 3–72 (1991) [3] Clerc, M.: The swarm and the queen: towards a deterministic and adaptive particle swarm optimization. In: Proceedings of the 1999 Congress on Evolutionary Computation, CEC 1999, vol. 3. IEEE (1999) [4] Thakur, M., Deep, K.: A new crossover operator for real coded genetic algorithms. Applied Mathematics and Computation 188(1), 895–911 (2007)


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[5] Diffie, W., Hellman, M.E.: Special feature exhaustive cryptanalysis of the nbs data encryption standard. Computer 10(6), 74–84 (1977) [6] Dorigo, M., Di Caro, G.: Ant colony optimization: a new meta-heuristic. In: Proceedings of the 1999 Congress on Evolutionary Computation, CEC 1999, vol. 2. IEEE (1999) [7] Eberhart, R.C., Shi, Y.: Comparing inertia weights and constriction factors in particle swarm optimization. In: Proceedings of the 2000 Congress on Evolutionary Computation, vol. 1, pp. 84–88. IEEE (2000) [8] Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks, vol. 4, pp. 1942–1948. IEEE (1995) [9] Kennedy, J., Eberhart, R.C.: A discrete binary version of the particle swarm algorithm. In: IEEE International Conference on Systems, Man, and Cybernetics, ’Computational Cybernetics and Simulation’, vol. 5, pp. 4104–4108. IEEE (1997) [10] Laskari, E.C., Meletiou, G.C., Stamatiou, Y.C., Vrahatis, M.N.: Evolutionary computation based cryptanalysis: A first study. Nonlinear Analysis 63(5-7), e823–e830 (2005) [11] Passino, K.M.: Bacterial foraging optimization. International Journal of Swarm Intelligence Research (IJSIR) 1(1), 1–16 (2010) [12] Price, K.V., Storn, R.M., Lampinen, J.A.: Differential evolution: a practical approach to global optimization. Springer, Heidelberg (2005) [13] Shi, Y., Eberhart, R.: A modified particle swarm optimizer. In: The 1998 IEEE International Conference on Evolutionary Computation Proceedings, IEEE World Congress on Computational Intelligence, pp. 69–73. IEEE (1998) [14] Shi, Y., Eberhart, R.: Parameter Selection in Particle Swarm Optimization. In: Porto, V.W., Waagen, D. (eds.) EP 1998. LNCS, vol. 1447, pp. 591–600. Springer, Heidelberg (1998) [15] Williamson, D.F., Parker, R.A., Kendrick, J.S.: The box plot: a simple visual method to interpret data. Annals of Internal Medicine 110(11), 916 (1989) [16] Yagmahan, B., Yenisey, M.M.: Ant colony optimization for multi-objective flow shop scheduling problem. Computers & Industrial Engineering 54(3), 411–420 (2008)

Health Diagnosis of Industrial Equipments through Used Lubricant Analysis Process: A Rule Based Inference Approach Surojit Ghosh1, Bijan Sarkar2, Subir Sanyal2, and Jyotirmoy Saha2 1 2

The Institution of Engineers, India Department of Production Engineering, Jadavpur University, Kolkata, India [email protected], [email protected], [email protected], [email protected]

Abstract. Any real-time engine diagnostic monitoring system deals with fault and off-nominal conditions as they are occurring. But prognostics are the ability to assess the current health of the machinery and predict the future health for a fixed time horizon or predict the time to failure of the machinery. Fault diagnosis of industrial machineries improves the quality of manufacturing as well as to reduce the cost for product testing. In modern manufacturing environment, a fast and reliable diagnosis system has turned into a challenging issue in the complex industrial atmosphere. In the present work, the diagnosis of bearing system has been considered as the platform of health monitoring system by used lubricant analysis process. Rule based inference system has been adopted in the present work, where possible characterized wear particles from the bearing system have been interpreted into the fuzzy inference mechanisms. Based on the proposed strategy, the possible maintenance policies have been taken into consideration. Keywords: Fuzzy System, Wear Particle Analysis, Fractal Mathematics, Image Analysis.

1 Introduction Most of the manufacturing organizations are quite motivated to get the accurate information from the production machines in order to deduce some key factors, which affect their margins with efficiencies. Even, the performance indicators like, uptime, downtime, cycle times etc. can be detected through this method. These indicators are quite useful to determine the overall efficiency of any plant or equipment of a manufacturing system, provided, the source of information / data must be accurate and dependable. The condition monitoring of machinery through a lubricating system has become an extensively applied diagnostic technology, which can ensure the operational effectiveness of any manufacturing organization. The effective maintenance program based condition monitoring through used lubricant analysis can determine

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both machine condition as well as lubricant condition too [2]. In such cases, lubricating oil may be used as a diagnostic medium that carries the wear particles generated from the surfaces. But doing analysis program of wear debris, the condition of the machine parts can be judged properly. The condition-monitoring program based on oil analysis has been updated over the past few decades. The most important factor is aging of machinery in machine diagnostics as it involves machine depreciation. The rates of change of machine components always depend upon the measurable parameters, where maintenance of lubricant plays a vital role, which has been shown in Fig.1. This kind of system can overcome all possible hazards at its optimum level so that a wider range of machine condition monitoring can be followed up by utilizing wear particle analysis [1].

Fig. 1. Aging factor of industrial machinery

2 Wear Particle Analysis Wear is the damage to a surface that generally involves the sufficient loss of materials and it occurs due to relative motion between that surface and the contacting substances. Plastic shear deformation of a particular surface is one of the sign of causing wear, which formed by shear fraction and leads to a scale like, topography [7]. Wear can also be accompanied by a number of other surface damage modes, such as extrusion, chip formation, tearing, brittle fracture, etc., basically, it is the complicated area, where a few predictive relationship can be established. It is quite well known phenomenon that the lubrication is one of the best mode of detection of wear amongst other techniques [4], but wear particle distributions may be characterized based on the features such as,

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Material Size Shape Concentration

The normalized wear rates for four mechanisms that cause a vast majority of abnormal wear in any industrial machinery, which has been shown in Fig.2, where the value ‘1’ has been considered as a reference and wear has been categorized depending on >1 or