Soft computing methods applied to condition monitoring and fault diagnosis for maintenance

Malfunctions in equipment and components are often sources of reduced productivity and increased maintenance costs in various industrial applications. For this reason, machine condition monitoring is being pursued to recognize incipient faults in the strive towards optimising maintenance and productivity. In this respect, the following lecture notes provide the basic concepts underlying some methodologies of soft computing, namely neural networks, fuzzy logic systems and genetic algorithms, which offer great potential for application to condition monitoring and fault diagnosis for maintenance optimisation. The exposition is purposely kept on a somewhat intuitive basis: the interested reader can refer to the copious literature for further technical details. Zio Enrico Soft computing methods applied to condition monitoring and fault diagnosis for maintenance 364 assume that the system‟s degradation level can only be known through periodic inspection as typical in safety systems such as those employed in nuclear plants [2]-[3], [26]-[27]; Kopnov [16] considers the case in which the system is continuously monitored and Lam [17] considers both cases. Another common assumption is to consider that repairs/replacements always restore the system to a „good-as-new‟ condition, which, in practice, may not be very realistic; Kopnov [16] has allowed also for partial recovery. The dynamic CBM policies for single-component systems whose condition can only be known through inspection, developed in [10], [12] and [19], are all based on control-limit rules which define when to repair/replace a component and when to schedule the next inspection. For the continuously inspected systems investigated by Kopnov [16], the two-level policies from the Inventory Theory have been adapted to the CBM problem of degrading systems. Semi-Markov processes are also considered; a death process is proposed for a unit subject to corrosion and a Markov chain is used for modelling fatigue crack growth. A common feature of the models discussed is that the state of the system is described as a state of a Markov process and then the analysis proceeds to finding analytically the probabilities of the various states. However, if the system is made of several multi-state components the analysis becomes excessively complicated. Simulation tools are hence needed when treating more complex systems. Bérenguer et al. [[4] have extended the work of Grall et al. [10] by investigating two-component deteriorating systems using simulation. Their maintenance model takes into consideration economic dependence between components and again the state of the system is only known through periodic inspections. Barata et al. [2] developed a stochastic degradation model for repairable multi-component systems and embedded its simulation within a maintenance optimisation scheme. The condition of each component is known continuously. The novelty of the model stems from the fact that the component‟s failures can occur not only because of excessive degradation which leads to a critical state of the system, but also because of random shocks which suddenly fail the system and whose occurrence probability is degradationdependent. While in some cases the system degradation level depends on the combination of many mechanisms and can only be known through inspection [4], [12], [12], [19], [26] there are other mechanisms such as fatigue and corrosion of structures in which deterministic laws are known and the uncertainty is on the value of the parameters that govern those laws. Regarding the deterioration models themselves, Hontelez et al. [12] give several examples, all of deterministic nature, from the civil engineering field. Grall et al. [10] use a model in which the degradation level increases randomly according to an exponential distribution. Degradation models describing fatigue and corrosion of metal structures are described by Guedes Soares and Garbatov in [23], [24]. The success of condition monitoring and conditionbased maintenance strongly relies on the capability of modelling the degradation processes and the corresponding plant dynamic responses under different configurations and conditions. However, the complexity and non-linearities of the involved processes are such that analytical modelling becomes burdensome, if at all feasible without resorting to unrealistic simplifying assumptions. For this reason, empirical modelling is becoming very popular since it does not require a detailed physical understanding of the processes nor knowledge of the material properties, geometry and other characteristics of the plant and its components and it does not resort to simplifying assumptions: the underlying dynamic model is identified by fitting plant operational data, with a procedure often referred to as „learning‟ or „training‟. Among the various techniques of empirical modelling, the so-called soft computing methods offer powerful algorithms for constructing non-linear models from operational data. As a fact, they are being used with increasing frequency as an alternative to traditional models in a variety of engineering applications including monitoring, prediction, diagnostics, control and safety. The main soft computing methodologies are Neural Networks (NNs), Fuzzy Logic Systems (FLSs) and Genetic Algorithms (GAs). These methodologies are inspired by biology and natural behaviour and provide potentially powerful tools for effectively tackling difficult multivariate, non-linear problems, which often cannot be solved with ease by means of traditional analytical or numerical methods. In the present lecture notes, we shall try to give a brief description of the concepts underlying the different methodologies and point out their main advantages and limitations. With this objective in mind, we shall refer our discussion to a multidimensional non-linear input/output mapping, for NNs and FLSs, or searching space, for GAs optimisation. NNs and FLSs are capable of establishing the existing non-linear input/output relationships, which map the inputs of a system to its outputs. They reconstruct the complex non-linear relations by combining multiple simple functions. More precisely, through an analogy with the functioning of the human brain, NNs form the shape of the mapping of interest by appropriately SSARS 2007 Summer Safety and Reliability Seminars, July 22-29, 2007, Gdańsk-Sopot, Poland 365 combining a large number of sigmoid, radial or other simple parameterised functions, which are adjusted (enlarged, shrunk, shifted, etc.) by means of appropriate parameters and synaptic weights [20], [21]. The great power of this technique lies in the fact that the adjustments can be made „automatically‟ through a training phase based on available input/output data: this training phase allows to adjust the NN-model parameters so as to obtain the best interpolation of the multivariate, non-linear functional relation between input and output. FLSs, on the contrary, partition the input/output spaces into several typically overlapping areas, whose shapes are established by assigned membership functions and whose mapping relationships are governed by distinct, simple IF-THEN rules [28], [13]. The great advantage of this method lies in the inherent capability of handling imprecise data and in the physical transparency and interpretability offered by this particular way of representing the underlying model relations. Finally, if the input/output multidimensional space is seen as a searching space in which the inputs are the decision variables and the outputs are the performance indicators of the search problem, the GAs offer a powerful method for evaluating a best input solution with respect to the optimisation (minimization or maximization) of the performance indicators of interest [9], [11]. The main advantages of the method are that the search is performed by manipulation of a population of points, contrary to classical methods which proceed from a single solution point to another, and that the search is solely based on the evaluation of the performance indicators, with no need of other information, e.g. of derivative nature. 2. Artificial Neural Networks Artificial neural networks (ANNs) are information processing systems composed of simple processing elements (nodes) linked by weighted connections. Their functioning is inspired by the biological neural networks. A biological neuron consists of dendrites, a cell body and axons (Figure 1a). The connections between a dendrite and the axons of other neurons are called synapses. In correspondence of each synapse, electric pulses from other neurons are transformed into chemical information which is input to the cell body: if the sum of the inputs received by the neuron through all its synapses exceeds a given threshold, then it fires an electric pulse which activates the neuron function. The network of all these neurons makes up the most essential part of the human brain and its operation enables the incredible variety of human activities. In synthesis, the function of a biological neuron is „simply‟ to output pulses, with the characteristics of a quasi-step switching function, according to a weighed combination of the multiple signals received from the other connected neurons. A second important function of the neuron is to appropriately modify the rate of transition through the different synapses to optimise the whole network. Figure 1. A biological neuron (a) and an artificial neuron model (b) [25] An artificial neuron (node) aims at simulating the operation of a biological neuron: thus, it accepts multiple inputs 1 2 , ,..., m x x x , it weighs them by means of adaptive synaptic weights, 0 1 , ,..., m w w w , and it simulates the switching function characteristic of the input/output relation to provide the output (Figure 1b). Connecting several artificial neurons together one obtains an artificial neural network which, by construction, constitutes an i