Mode diagnostics of pipeline systems of the energetics

. The paper proposes a method for diagnosing gradual failures in pipeline power systems, based on tracking the dynamics of flow regime parameters. The method also makes it possible to promptly adjust the coefficients of a mathematical model of the system objects. Conclusions are made based on the analysis of the entire set of measurements, which are considered random variables due to measurement errors. Conclusions are made based on the analysis of the entire set of measurements, which are considered random variables due to instrumental errors. Examples of a gas pumping unit and a complex looped gas pipeline system are given. Calculations are performed using standard software.


Introduction
The information base for monitoring the state of gas and oil pipeline transportation systems is constantly being improved. However, its increased potential is actually not fully used. Mode diagnostics (MD) is an effective way to recognize gradual failures and also to quickly assess the technical condition of equipment. It, as a rule, does not require significant investment. The paper proposes the MD methodology. The constructed models are based on the maximum likelihood method; their computer implementation does not require the development of specialized digital procedures. To test the methods, computational experiments were carried out under the conditions of both stationary and unsteady fluid flow.

Operational diagnostics of the gas compressor (GC)
Standard devices measure the following mode parameters: Here ()  Q is the efficiency, ( , )  Qn -is the pressure characteristic,  is the compression ratio, n is the number of revolutions of the centrifugal blower, m is the polytropic index. In addition to (1), the mathematical model of the compressor includes a number of technological limitations in the form of inequalities: maximum pressure, maximum discharge temperature and power.
The operating rules provide for various operations to monitor its technical condition based on diagnostic indicators, the dynamics of which allows one to assess the state of various GC subsystems. In contrast to these particular tasks of technological control, the problem considered in this paper refers to the diagnostics of GC. It takes into account all the information on standard measurements of the mode parameters, all physical (thermodynamic) relations (1) connecting them, and limitations determined by the design features of the unit.
CR the inverse matrix of the covariance matrix R . The task of the MD is to estimate one or two (depending on the formulation of the problem) adaptation coefficients ,  N kk on the basis of a onetime series of measurements and, if the coefficient is significantly less than 1, to conclude that the equipment is worn out and the GC model needs to be adjusted. MD formalization has the form of a mathematical programming problem with conditions in the form of equalities (1) and inequalities due to technological restrictions. Here is the vector of the estimated parameters. Typically, errors are independent and the matrix R is diagonal. An iterative process with Newtonian linearization at each iteration step was used for the solution. It is very important to check on factual material how the iterative process converges depending on the initial approximation. You can get an idea of this by conducting a computational experiment. Such an experiment was carried out for two types of GCs NTs -16/76 (with a power of 16 MW) and 2N -25 -76 (with a power of 25 MW). The main conclusion based on the experiment: the computational procedure adequately estimates the adaptation coefficients of the mathematical model. In the case of 2 estimated coefficients, the computational procedure has resulted to the correct, one and the same, result when varying the initial approximation and variances that determine the quality of the initial information for simulating.

Mode diagnostics GPS at steady flow
Let us now consider the pipeline system of the main gas supply (Fig. 1). The example will illustrate the MD methods applied to a large-scale gas pipeline system (GPS). GPS in Fig. 1 is a fragment of the UGSS RF, a complex gas pipeline branch with metrological support, the real modes of which are sufficient for testing diagnostic methods. The actual problem of the operational control of the GPSs is the timely recognition of the formation of hydrates or condensate deposits. These phenomena cause an increase of hydraulic resistance of the pipes and lead to a partial failure of the pipeline. To take them into account, the actual coefficient of hydraulic resistance fact  , or the coefficient of efficiency  theor fact K  , is entered into the mathematical models of the pipeline. In design calculations, it is assumed 0,95  K . A significant decrease in K -a signal to clean the pipe. To control the resistance of pipelines it is advisable to monitor the dynamics of the entire set of measured operating parameters of the GPS. Despite the great interest to the problems of identification and routine diagnostics of GPS [1,[3][4][5], the practical implementation of the research results leaves much to be desired. In this paper, the MD is applied to the GPS (Fig. 1) for both stationary and unsteady flow regimes. To analyze the mode, the methods of the theory of hydraulic circuits are used [1,6]. Identification problems constitute one of the sections of this theory [7]. In the accepted notation, the stationary flow model is written in the form , is the vector of external inflows / withdrawals, A is the complete matrix of incidents, A is the matrix of incidents with linearly independent rows, Λ is the diagonal matrix with elements equal to the generalized resistance coefficients of pipelines, X -diagonal matrix with elements ; 1, , Stationary flow identification can be carried out according to various principles. The fewer parameters are identified, the greater the chances of successfully solving the problem. To study the features of the computational process on the considered GPS, a number of experiments were carried out. From the measured values of inflows / withdrawals in sources and consumers, the flow distribution (vector x ) was determined according to the equations of the 1st Kirchhoff's law. This flow distribution is named * x . The values of the efficiency coefficients were evaluated according to the criterion arising from the principle of maximum likelihood (the minimum of the sum of the squares of the discrepancies between the solution and the observed values of the operating parameters). Measurement errors are again assumed to be distributed according to the normal law. If * Y the vector of measured parameters, and R its correlation matrix, then the criterion is written in the form (2). To estimate the efficiency coefficients When choosing an initial estimate, information that is not included in the formalization of the mathematical programming problem should be used as much as possible. We first made an assumption, based on technological assumptions, that the efficiency ratios of all sites are equal ; 1, ,  In this case, heuristic selection turned out to be extremely successful. The example shows that, knowing the features of the functioning of the GPS, one can expertly outline several options for the set of identified coefficients and expect that among the compared options there will be one (or several) that will be a good approximation to the desired solution and can be used as initial estimate for more precise procedures.
In the case of a less successful initial selection, the following steps should be taken to consistently improve the initial estimate. From the assumption that the efficiency factors for all pipelines are equal  , go to two values ,    , that is, divide all pipelines into 2 groups with the same efficiency factors in the group. It is expedient to divide the partition according to the contribution of the pipelines to the residual sum of the squares of the criterion where Ŷ is the solution obtained with the current approximation of the desired vector. Then the procedure can be continued, sequentially increasing the number of different values of the efficiency coefficients, that is, dividing the pipelines into 3, 4, etc. groups.

Mode diagnostics of GPS at unsteady flow regime
The operating parameters of the gas flow are constantly changing over time. Taking into account the nonstationarity in the MD model increases the degree of its adequacy. For unsteady gas flows in pipes, it is advisable to use a lumped parameter model (LPM), which describes well the normal mode of gas flow [1,5]. In this model, each arc j of the graph is characterized not by one, but by two values of the flow rate: at the beginning s j q and end f j q of the arc. In this case, the 1st equation in system (3) is replaced by f s s f i i i  A q A q Q , the 2nd one -by a finitedifference scheme for solving ordinary equations of the LPM [1,6]. These two vector equations play the role of equality constraints in the mathematical programming problem for evaluating the vector K of efficiency coefficients. The likelihood function in this case will depend on measurements over the entire observation period. The set of data acquisition times will be denoted by * Т . Due to the independence of measurements at different times, the covariance matrix R for all observations is equal * t tT    RR , and, therefore, * t tT    СС . To estimate K , we obtain the conditional minimization problem (3) with equality constraints. To solve it, an iterative process with Newtonian linearization is used. To test the method, the de facto daily graphs of the GPS (Fig. 1) fig. 2 of out all solution components 2 functions are represented. It can be seen that the solutions of the 1st stage (curves 2) differ markedly from the measurements (curves 1) for some t . To determine what corrections it is advisable to make in the assumption about the estimated vector K , let us analyze the residual sum of squares   it is expedient to introduce the efficiency coefficients of the pipelines supplying gas to these consumers into the number of estimated coefficients of the model (Fig.  1, pipelines 34 and 30 km long). Let's designate these values 11 12 , KK . At the 2nd stage of the computational experiment, when evaluating 3 unknowns, the following result is obtained: 11 120 ,917; 0,925 KK    , the remaining coefficients are equal 1 10 0,918 K    . The obtained solutions -curves 3 (Fig. 2) -visually almost do not differ from measurements (curves 1). For a quantitative characteristic of the mismatch "fact -calculation", we introduce the distance between