Description

The present invention relates to a method for operating a distribution network having a certain network topology using N sensors for sensing wavefront characteristics, each of said N sensors being located at a certain measurement location in the distribution network. The present invention further relates to a computer program product and to a device for operating a distribution network having a certain network topology. Moreover, the present invention relates to a distribution network comprising a plurality of pipe segments for distributing a certain load and such a device for operating the distribution network.

Distribution networks, like water supply networks or heat supply networks, may be subject to failure due to various reasons. For example, failures of particular segments of the distribution network may lead to interrupts in the supply for consumers or damages of the infrastructure, like roads and other properties. Therefore, together with the task of minimizing the time required to correctly detect, localize and isolate a damaged segment in the distribution network, there is a need to minimize the risk of a failure in the distribution network.

Conventional models and approaches for evaluating risks of failures in pipe segments of a distribution network are known from references [1] to [4],

It is an object of the present invention to enhance the operation of a distribution network.

According to a first aspect, a method for operating a distribution network having a certain network topology using N sensors for sensing wavefront characteristics is suggested. Each of said N sensors is located at a certain measurement location in the distribution network. The method comprises the following steps a) , b) and c) : a) obtaining values of transient event parameters of a certain transient event in the distribution network using at least a subset of the N sensors,

b) determining a risk factor indicating a hazard in the distribution network in dependence on the obtained values for the transient event parameters and actual values of network parameters being indicative for the distribution network, and c) executing one of a number of actions at the distribution network in dependence on the determined risk factor .

For example, the distribution network is a water distribution network, an oil distribution network, a gas distribution network or a heat distribution network. The distribution network may also be referenced as network.

A hazard may be a real or actual damage of the distribution network, like a pipe congestion or a pipe burst, or a high probability of a damage of a pipe or pipe segment in the distribution network. The pipe segment may also be referenced as segment .

Examples for transient events include leaks, valve openings, valve closures, pump starts or pump stops. Moreover, examples for the transient event parameters include a magnitude of the certain transient event, a location of the certain transient event in the distribution network and/or an event type of the certain transient event in the distribution network. The event type may also be referenced as type.

Depending on the amplitude of the transient event, the wavefront caused by said transient event is detectable by a certain subset of the sensors or by all sensors in the distribution network. Thus, this subset of the sensors is able to obtain values of the transient event parameters of a certain transient event. In other words, different transient events may be detectable by different subsets of the sensors located at different measurement locations in the distribution network.

In particular, the topology of the distribution network is known a priori, in particular before the method including steps a) to c) is executed. In particular, information indicating the network topology as part of the network parameters is stored in a memory, wherein said information may be used in said step b) of the method.

Further, the network parameters may include information about the age of the pipes, the material of the pipes and the average and maximum static loads in the distribution network. Furthermore, the network parameters may include logged or historical data of the distribution network.

Executing one of the actions according to step c) may include to provide a replacement recommendation for replacing a pipe or a pipe part or to provide an alarm to an operator or a service personnel of the distribution network. Moreover, said executing a certain action may include logging the determined risk factor or determined risk factors. Further, a replacement recommendation or an alarm may be generated or triggered using the logged determined risk factors.

Furthermore, a certain action may include to provide a visual representation of the distribution network, like a heat map of a graph representing the distribution network and indicating potential hazards and determined risk factors, for the operator or service personnel of the distribution network.

By using not only the actual values of the network parameters, but also the. obtained values for the transient event parameters, the risk factor for a hazard in the distribution network can be determined with a higher accuracy. Determining risk factors with a higher accuracy results in lowering the costs for the maintenance of the distribution network and in enhancing the planning of network rehabilitation strategies.

In the following, several embodiments for the method for operating a distribution network are described.

According to an embodiment, the risk factor is determined in dependence on the obtained values of the transient event parameters, the actual values of the network parameters, load- related factors of a load distributed by the distribution network and external factors describing an environment of the distribution network. According to a further embodiment, the transient event parameters include a magnitude of the certain transient event, in particular at a certain measurement location or at certain measurement locations, a location of the certain transient event in the distribution network and/or an event type of the certain transient event in the distribution network.

According to a further embodiment, the step a) includes:

obtaining values of the transient event parameters of a plurality of certain transient events in- the distribution network using at least said subset of N sensors.

According to a further embodiment, the step a) includes:

sensing wavefront characteristics caused by the certain transient event in the distribution network using at least said subset of the N sensors,

collecting signals from said subset of the N sensors, said signals being indicative of the sensed wavefront characteristics, and

processing the collected signals for obtaining said transient event parameter.

According to a further embodiment, the step b) includes:

providing a model for modeling a hazard in the distribution network, said model being time-dependent and using a parameter set at least representing the network parameters and the transient event parameters,

modeling an actual hazard by applying determined actual values at least including the obtained values of the transient event parameters and the actual values of the network parameters for the parameter set to the provided model, and

determining the risk factor in dependence on the modeled actual hazard.

According to a further embodiment, the step b) includes:

dividing the distribution network into pipe segments, allocating each of the pipe segments to one of a plurality of M groups according to at least one categorical parameter, with M ³ 2, and for each of said M groups, the following sub-steps i) to iii) are executed:

i) providing a model for modeling a hazard in the pipe segments of the group, said model being time-dependent and using a parameter set at least representing the network parameters and the transient event parameters,

ii) modeling an actual hazard by applying determined actual values at least including the obtained values of the transient event parameters and the actual values of the network parameters for the parameter set to the provided model, and

iii) determining the risk factor for the pipe segments of the group in dependence on the modeled actual hazard.

According to a further embodiment, the pipe segments are disjunct to other and each of the pipe segments is homogenous at least regarding pipe material and pipe diameter.

According to a further embodiment, the model for modeling the actual hazard uses a Cox regression.

According to a further embodiment, in the Cox regression, the below-mentioned formula for modeling the time-dependent and parameter-set-dependent actual hazard h(t,x) is used:

In this formula, t designates time, x designates the parameter set as a vector, ho(t) designates a base line hazard due to time t and b designates a vector of coefficients for the parameter set.

According to a further embodiment, each of the sensors is a high-rate pressure sensor. For example, each of the sensors has a sampling . rate of 100 Hz or greater, in particular of 200 Hz or greater.

According to a further embodiment, the step b) of determining the risk factor is executed by a central processor unit of the distribution network.

According to a further embodiment, the method includes a step of determining the location of the certain transient event in the distribution network in dependence on the differences of detected arrival times of the wavefront detected by the sensors located at said subset of the measurement locations and positions of the measurement locations.

In particular, the positions of the measurement locations are part of the a priori known network topology. Thus, the positions of the measurement locations are known before the above-mentioned method steps are executed.

According to a further embodiment, for each possible sensor pair of the N sensors, the time shift between the arrival times at the two sensors of the sensor pair is determined by cross-correlating the wavefronts received at said two sensors.

According to a further embodiment, the event type of the transient event in the distribution network is classified as a leak, as a valve opening, as a valve closure, as a pump start or as a pump stop using the determined location of the transient event in the distribution network, using the detected arrival times of the wavefront detected by the sensors located at said subset of the measurement locations, and using the certain network topology of the distribution network.

According to a further embodiment, the risk factor is determined in dependence on the actual values of the network parameters, on the actual values of load-related factors of a load distributed by the distribution network including the obtained values of the transient event parameters, and external factors describing an environment of the distribution network.

The network parameters may comprise meta information, said meta information particularly including segment age, segment material, corrosion level and the like.

The load-related factors may include pressure transients and the accumulated flow rate through the respective segment. Moreover, the external factors may include soil conditions and the installation nature. The installation nature may describe an installation under street or under a heavy traffic area, for example. The above factors may be also referenced as covariates. The covariates may be continuous, discrete or categorical. It may be noted, that the covariate may be converted into a discrete one or a categorical one by using means of ranges.

According to a further embodiment, the step b) includes:

providing a model for modeling a hazard in the distribution network, said model being time-dependent and using a factors vector representing the network parameters, the load-related factors including the transient event parameters, and the external factors,

modeling an actual hazard by applying determined actual values at least including obtained values of the load-related factors including the transient event parameters, the actual values of the network parameters and the actual values of the external factors for the factor vector to the provided model, and

determining the risk factor in dependence on the modeled actual hazard.

According to a -further embodiment, the step b) includes:

dividing the distribution network into J\T interconnected pipe segments S _ir where designates the i ^th pipe segment with i. Vi = {1,2, ...N}, wherein the pipe segments are considered disjunct to other and each of the pipe segments is homogenous at least regarding pipe material and pipe diameter.

Said factors may be also referred to as covariates.

According to a further embodiment, for modeling the lifetime of a pipe segment, the formula

is used for modeling the time-dependent actual hazard associated with the pipe segment S _a ,

where x _Sa is the factor vector, t is the time at which the actual hazard for the segment S _a is to be evaluated, b is the coefficients vector of the model, ) is the function used to compute the actual hazard being dependent on the used model, e.g. a Cox regression model or a logistic regression model. According to a further embodiment, the model for modeling the actual hazard uses a Cox regression model, wherein, in the Cox regression, the formula

hs _a ( ^x s _a , t\fi) = h ₀ () exp{/?¾J ... (3)

is used, where h ₀ (t) designates a base line hazard due to time t .

The Cox regression model is a semi parametric model. In particular, it quantifies the baseline hazard, which is a hazard resulting from solely aging of the component (here pipe segment) in a nonparametric manner. Then, it uses a parametric method for either accelerating or deaccelerating the hazard profile based on the factors.

According to a further embodiment, the model for modeling the actual hazard uses a logistic regression model, wherein, in the logistic regression model, the formula

is used, where Pf\s _a designates the probability of failure of the pipe segment S _a .

The logistic regression is a sigmoid function whose range is limited in the range [0, 1] . Consequently, it is appropriate for being used in modeling failure probability of a component (here a pipe segment) . It is mentioned that in this model, time is also considered as a part in the factors vector ¾¾ (an additional covariate) , and has a corresponding coefficient in the vector b. As can be noticed in the above equation, this method is a parametric method, whose output can be learnt for historical data via methods of expectation maximization (EM) , or iteratively reweighted least square (IRLS) method.

According to a further embodiment, the coefficients vector b is learnt based on historical data. In particular, learning the hazard model represents using historical data for inferring the coefficients vector b. For factors such as pipe diameter and length, they are straightforward to be incorporated in the model, that is, they affect only their corresponding segment, and possess no effect on the other segments. However, the transients events do affect the other segments - with respect to the segments on which they took place. This is due to the fact that those events generate pressure transients that propagate through the network and are subject to being reflected by some components of the network such as valves and/or fittings. Therefore, when a transient event takes place, it may affect other parts of the network.

According to a further embodiment, the model is adapted for modeling reflections of the transient event in the distribution network and/or the factors vector includes factors relating to pressure transients of different types. This is discussed in detail for the example of pressure transients as an example for transient events, in the following:

Pressure transients yield into fatigue, a phenomenon that accelerates the failure of a pipe segments Pressure transients happen due to several reasons, for example, bursts, valve operation (opening and/or closing) , pumps operation (start up and/or shut down) and the like. Regardless of why transients happen, they propagate through the pipe segments connected to the segment where the event took place. This affects not only the segment on which they happened, but also on the other connected segments with different levels of effect due to the decay of the transients wave amplitude as the transients travel through the network.

In addition to the propagation of pressure transients waves, they are also subjected to being reflected by some parts of the network such as valves and fittings. And hence, those reflections possess an effect on the developing hazards on the network. Also, these reflections also travel through the connected segments and are again subjected to reflections. For tractability reasons, only the first-order reflections are considered in the following, that is to say, only propagation of original pressure transients and first reflections propagation are considered. However, relaxing this approach to include more phases of reflections is possible.

Firstly, the segments and reflection surfaces {<5 _a ,K _a } that affect the particular segment of interest (S _a) are defined as: ·*« = {««.*«}. (5)

where :

_< A _a — is the set of all segments and reflection surfaces that affect the segment of interest S _a ,

<S _a — is the set of all segments, where events happening will affect the segment of interest S _a , and

SR _a — is the set of all reflection surfaces that affect the segment of interest S _a

<S _a depends on the distances between the segment of interest S _a and the rest of the segments in the network. Further, fR _a depends on the topology of the network, as the topology gives the locations of these reflection surfaces relative to the segment of interest S _a . For example, one way to find <3 _a is to consider the segments and reflection surfaces whose respective distance relative to the segment of interest S _a is less than a pre-defined threshold.

To incorporate the effect of the pressure transients on a segment of interest S _a , firstly, the pressure transients are divided into € types. For example, these types can include: i. Segment burst

ii. Valve operation (opening/ closing)

iii. Pump operation (startup/ shut down)

Then, the factors vector x _Sa - in addition to the aforementioned · factors - includes factors related to pressure transients ,

Where :

Y _$a — set of factors vector representing pressure transients as covariates affecting the segment of interest (S _a) , Y _5a G — the x ^th factor representing the x ^th type of pressure transients on the segment of interest (S _a) , x ={1,2,... }.

Therefore, to incorporate the effect of the pressure transients of different types on the hazard profile of the segment of interest (S _a) , it may be considered that the effect of the transient decays with the traveled distance. To model this, a radial basis function (RBF) may be used.

Consequently, the following formulation is proposed to evaluate the elements in Y _$b .

Where :

— is the amplitude of the i ^th pressure transient wave of the x ^th type,

Fr >a _> $ί) ~ is the RBF describing the decay of the effect of the propagated pressure transient happening at segment Si on the segment of interest S _a , the RBF describing the decay of the effect of the reflected pressure transient {M^fr 3ί, 1^ ) from surface Jlj on the segment of interest S _a .

It may be mentioned that the reflection happens on the wave once it reaches the reflection surface. That is, when the x ^th type event happens at segment _t with amplitude it first propagates to the reflection surface Rj whilst decaying to be , then it is reflected back from the reflection surface Jlj to the segment of interest S _a decaying as per the reflection

Several RBF may be used, one example is the Gaussian RBF, the corresponding RBF used in equation (7) are defined as in equations (8), (9), and (10).

Where : is the traveled distance through the network from the event location (c _E _ ) to the center coordinates of the segment of interest S _a ,

— c _Es J— is the traveled distance through the network from the event location (c _{Es )} to the reflection surface R _j , is the traveled distance through the network from the reflection surface l _j to the center coordiantes of the segment of interest S _a ,

i _p — is the width parameter which controls the decay rate of the propagated x ^th type pressure transient,

(x)2

t ^— is the width parameter which controls the decay rate of the reflected x ^th type pressure transient.

It should be mentioned that for long segments, virtual segmentation may be used to obtain more accurate and high resolution results. More specifically, a long segment can be segmented into several shorter segments, so that the measure of the traveled distance is more appropriate for being used in equations (8), (9) and (10).

Equation (7) encompasses the width parameters These can be estimated based on field experiments. It may be mentioned though, that equations (8), (9) and (10) describe one type of RBF, namely, Gaussian RBF, however, other types can be used such as thin plate spline (TPS-RBF) to give an example .

The effect of the width parameter the result of the RBF the output value 0 is shown in Fig. 7. In Fig. 7, distances on the x axis are taken in both direction relative to the event location. Further, in Fig. 7, curve VI

(x)2 (1)2

designates t , curve V2 designates t _t curve V3 designates t^ ² , and curve V4 designates t^ ² .

Moreover, as an illustration example, let's assume a hazard model with the following covariates:

1. Segment material type (covariate x _x) .

2. Segment diameter (covariate x ₂₎ . 3. Segment length (covariate x ₃₎ .

4. Valve operation transients (covariate x ₄ ) .

5. Pump operation transients (covariate x ₅ ) .

6. Bursts transients (covariate x _{6 )} .

In this example, three types of pressure transients are considered, i.e. { = 3. The total number of covariates is 6, hence, the covariates vector for segment S _a is x _Sa , such that E l ⁷ excluding time and x _Sa € K ⁸ including time, defined as follows:

In equations (11) and (12), the covariates related to pressure transients can be linked to equation (7) as follows:

Another measure of the failure rate can be of interest, such as survival rate ^and probability of failure.

These can be obtained from the hazard rate as follows:

Additionally, the probability of failure can be calculated as follows :

Where :

Pf\s _a (t)— is the probability that segment S _a will have failed before time t.

The present scheme described so far quantifies the risks associated with pipe segments, and consequently with the network .

In the following, recommendations regarding segment replacement in the network are provided. This poses the question of whether to place a segment or not and at what failure probability. Since the risk may be quantified in a probabilistic manner, the replacement recommendation may be considered bearing in mind the uncertainty of the failure.

It is proposed to utilize tools of decision making under uncertainty. In table (1), a decision-cost matrix is shown. That is, two actions can be taken (replace, not replace) , whilst two results might happen (fail, not fail) . This results in 4 potential scenarios.

Table 1: decision-cost matrix

Where:

^iiC ~ is the cost taking the action of replacing the pipe segment at time t and it actually fails at t

A _i2 (.t) ^— is the cost taking the action of replacing the pipe segment at time t and it actually does not fails at t

the cost taking the action of not replacing the pipe segment at time t and it actually fails at t

s the cost taking the action of not replacing the pipe segment at time t and it actually does not fails at t

Pi(t)— probability the pipe segment will fail at time t

p ₂ ( ~ probability the pipe segment will not fail at time t

The expected cost of each action (replace or not replace) is calculated as follows:

Where:

^[^ c _i C _t) ] ^— i- ^s th* ³ expected cost of taking action a _έ at time t i ^s the cost of taking action a* from the set of potential actions ( _< A ) at time t

The recommended action is the one that minimizes the expected cost as in equation (17):

Where :

a ^* (t)— is the recommended action at time t.

Additionally, to recommend the time of replacement, the time at which the replacement expected cost becomes less than the not-replacement expected cost is found as in equation (18) is solved and given as the recommended time of replacement.

T = arg

Where :

T— is the recommended time of segment replacement

According to a second aspect, a computer program product is suggested, wherein the computer program product comprises a program code for executing the method of the first aspect or of one of the embodiments of the first aspect when the program code is run on at least one computer.

A computer program product, such as a computer program means, may be embodied as a memory card, USB stick, CD-ROM, DVD or as a file which may be downloaded from a server in a network. For example, such a file may be provided by transferring the file comprising the computer program product from a wireless communication network.

According to a third aspect, a device for operating a distribution network having a certain network topology is suggested. The device comprises:

a plurality N of sensors for sensing wavefront characteristics, each of said N sensors being located at a certain measurement location in the distribution network, wherein at least a subset of the N sensors is configured to obtain values of transient event parameters of a certain transient event in the distribution network, a determining unit for determining a risk factor indicating a hazard in the distribution network in dependence on the obtained values for the transient event parameters and actual values of network parameters being indicative for the distribution network, and

an executing unit for executing one of a number of actions at the distribution network in dependence on the determined risk factor.

In particular, the device may be or may include a computer- aided or computer-related system or a computer system.

The respective unit, e.g. the determining unit or the executing unit, may be implemented in hardware and/or in software. If said unit is implemented in hardware, it may be embodied as a device, e.g. as a computer or as a processor or as a part of a system, e.g. a computer system. If said unit is implemented in software it may be embodied as a computer program product, as a function, as a routine, as a program code or as an executable object.

The embodiments and features according to the first aspect are also embodiments of the third aspect.

Further possible implementations or alternative solutions of the invention ^' also encompass combinations-that are not explicitly mentioned herein-of features described above or below with regard to the embodiments. The person skilled in the art may also add individual or isolated aspects and features to the most basic form of the invention.

Further embodiments, features, and advantages of the present invention will become apparent from the subsequent description and dependent claims, taken in conjunction with the accompanying drawings, in which:

Fig. 1 shows a sequence of method steps of a first embodiment of a method for operating a distribution network;

Fig. 2 shows a schematic diagram of an example for a distribution network; Fig. 3 shows a sequence of method steps of a second embodiment of a method for operating a distribution network;

Fig. 4 shows a diagram illustrating the distance-dependent decay of the transient effects to a distribution network;

Fig. 5 shows a schematic block diagram of an embodiment of a device for operating a distribution network;

Fig. 6 shows a sequence of method steps of a third embodiment of a method for operating a distribution network; and

Fig. 7 shows a schematic diagram illustrating the effect of the width parameter in RBF on the output value.

In the Figures, like reference numerals designate like or functionally equivalent elements, unless otherwise indicated.

In Fig. 1, a sequence of method steps of a first embodiment of a method for operating a distribution network 10 having a certain network topology using sensors 31 - 33 for sensing high-speed wavefront characteristics is shown. Each of said N sensors 31 - 33 is located at a certain measurement location LI - L3 in the distribution network 10. The distribution network 10 may be a water distribution network, an oil distribution network, a gas distribution network or a heat distribution network, for example.

In this regard, Fig. 2 shows a schematic diagram of an example for the distribution network 10. In particular, Fig. 2 shows only a small part of such a distribution network 10. The distribution network 10 of Fig. 2 has a plurality of pipes 20 which are adapted to conduct a liquid, like water or oil.

Without loss of generality, the number N of sensors 31 - 33 is three (N = 3) in Fig. 2. Generally, N may be a positive integer, for example in a water distribution network N may be greater than 1,000. Each of the sensors 31 - 33 for detecting values of transient event parameters of a certain transient event E has a sampling rate of 100 MHz or greater. Thus, the sensors 31 - 33 are high-rate pressure sensors. In the example of Fig. 2, a burst of one of the pipes 20 as an example of a transient event E is depicted. The different paths of the pressure wave propagation caused by said burst E are indicated in Fig. 2 by PI, P2, and P3. In the example of Fig. 2, a first sensor 31 is located at measurement location LI, a second sensor 32 is located at measurement location L2 and a third sensor 33 is located at measurement location 33.

The embodiment of the method according to Fig. 1 has the following methods steps S10 - S30:

In step S10, values of transient event parameters of a certain transient event E in the distribution network 10 are obtained using at least a subset of the N sensors 31 - 33. For example, each of said subset of sensors 31 - 33 senses wavefront characteristics caused by said certain transient event E. In dependence on said sensed wavefront characteristics, the values of the transient event parameters are generated or created. Examples of the transient event parameters include a magnitude of the certain transient event E, in particular at the respective certain measurement location LI - L3 of the certain sensor 31 - 33, a location of the certain transient event E in the distribution network 10 and/or an event type of the certain transient event E in the distribution network 10. Examples of the event type include a leak, a congestion, a valve opening, a valve closure, a pump start and a pump stop.

In step S20, a risk factor indicating a hazard in the distribution network 10 is determined in dependence on the obtained values for the transient event parameters and actual values of network parameters being indicative for the distribution network 10.

The network parameters may include meta-information about the distribution network 10, like pipe age, pipe material, pipe diameter, corrosion-related feature and others. Further, input parameters for determining the risk factor may include load- related factors of the load by the distribution network 10 and external factors describing an environment of the distribution network 10. The external factors may include soil conditions, temperature and precipitation and the like. The load-related factors may exe plarily include parameters of the load as such, like a density value of the load.

In step S30, one of a number of actions at the distribution network 10 is executed in dependence on the determined risk factor. Executing one of the actions may include to provide a replacement recommendation for replacing a pipe or a pipe part or to provide an alarm to an operator or to service personnel of the distribution network 10.

Moreover, said executing a certain action may include to log the determined risk factor or determined risk factors over time. Further, a replacement recommendation or an alarm may be generated or triggered from the logged determined risk factors .

Furthermore, a certain action may include to provide a visual representation of the distribution network 10, e.g. in form of a heat map indicating potential hazards and allocated risk factors, to the operator or to service personnel of the distribution network 10.

Fig. 3 shows a sequence of method steps of a second embodiment of a method for operating a distribution network 10. The second embodiment of Fig. 3 is based on the first embodiment of Fig. 1, wherein method step S10 of Fig. 1 is embodied by method steps S-ll to S13 according to Fig. 3 and method step S20 of Fig. 1 is embodied by method steps S21 - S23 according to Fig. 3.

In this regard, method step S10 includes steps Sll - S13:

In step Sll, wavefront characteristics caused by the certain transient event E in the distribution network 10 are sensed using at least said subset of the N sensors 31 - 33.

In step S12, signals from said subset of the N sensors 31 - 33 are collected. Said signals are indicative for the sensed wavefront characteristics.

In step S13, the collected signals are processed for obtaining said transient event parameters. For example, said processing may be executed by a central processing unit of the distribution network 10. As indicated above, method step S20 of Fig. 3 includes steps S21 - S23 :

In step S21, a model for modeling a hazard in the distribution network 10 is provided. Said model is time-dependent and uses a parameter set at least representing the network parameters and the transient event parameters.

In step S22, an actual hazard is modeled by applying determined actual values at least including the obtained values of the transient event parameters and the actual values of the network parameters for the parameter set to the provided model.

In step S23, the risk factor is determined in dependence on the modeled actual hazard.

Particularly, said step S20 may include to divide the distribution network 10 into pipe segments to allocate each of the pipe segments to one of a plurality of M groups according to at last one categorical parameter (M ³ 2) . Then, the following sub-steps i) to iii) may be executed:

i) providing a model for modeling a hazard in the pipe segments of the group, said model being time-dependent and using a parameter set at least representing the network parameters and the transient event parameters,

ii) modeling an actual hazard by applying determined actual values at least including the obtained values of the transient event parameters and the actual values of the network parameters for the parameter set to the provided model, and

iii) determining the risk factor for the pipe segments of the group in dependence on the modeled actual hazard.

In particular, the pipe segments are disjunct to each other and each of the pipe segments is homogeneous at least regarding pipe material and pipe diameter. In particular, the model uses a Cox regression. In the Cox regression, the formula

h(t, x) = h ₀ (t) ex r[b ^t c] ... (19) is used for modeling the time-dependent and parameter-set- dependent actual hazard h(t,x), where t designates the time, x designates the parameter set as a vector, ho(t) designates a base line hazard due to time t and b designates a vector of coefficients for the parameter set.

The parameter set x may be formulated as x = [xi, ..., x _P ] ^T , wherein x _p designates at least one transient event parameter, for example a pressure transient.

The transient event E in the distribution network 10 represented by said pressure transient x _P effects the segments of the distribution network 10 where it happened the most, and its effect fades away as the travel distance increases. In the below-mentioned formula this is controlled via the exponent k, i.e. the larger k is, the faster the decay of the transience effect with the travel distance is.

k E M _³ o ... (22)

In above formulas, M designates the magnitude of the pressure transient, and di designates the distance from the location of the transient event E to the center of the i-th segment Si of the distribution network 10.

In this regard, Fig. 4 shows a diagram illustrating the distance-dependent decay of the transient effects to hazards in the distribution network 10. In Fig. 4, the x-axis shows the distance d from the location of the transient event E in the distribution network 10, and the y-axis shows the exponent k of above-noted formulas.

In said Fig. 4, curve CO shows the curve progression for k=0, curve Cl shows the curve progression for k=l, curve C2 shows the curve progression for k=2, and curve C3 shows the curve progression for k=3.

Moreover, Fig. 5 shows a schematic block diagram of an embodiment of a device 50 for operating a distribution network 10, as depicted in Fig. 2. The device 50 of Fig. 5 shows a plurality 51 of sensors 31, 32, 33 for sensing wavefront characteristics. Each of the sensors 31 - 33 is located at a certain measurement location LI - L3 in the distribution network 10 (see Fig. 2). At least a subset of the sensors 31 - 33 is configured to obtain values of transient event parameters of a certain transient event E in the distribution network 10 (see Fig. 2).

Furthermore, the device 50 includes a determining unit 52 and an executing unit 53.

The determining unit 52 is configured to determine a risk factor indicating a hazard in the distribution network 10 in dependence on the obtained values for the transient event parameters and actual values of network parameters being indicative for the distribution network 10.

The executing unit 53 is configured to execute one of a number of actions at the distribution network 10 in dependence on the determined risk factor.

Fig. 6 shows a· sequence of method steps of a third embodiment of a method for operating a distribution network 10. The third embodiment of Fig. 6 is based on the first embodiment of Fig. 1, wherein method step S10 of Fig. 1 is embodied by method steps Sll to S13 according to Fig. 6 and method step S20 of Fig. 1 is embodied by method steps S20a - S20c according to Fig. 6.

In this regard, method step S10 includes steps Sll - S13:

In step Sll, wavefront characteristics caused by the certain transient event E in the distribution network 10 are sensed using at least said subset of the N sensors 31 - 33.

In step S12, signals from said subset of the N sensors 31 - 33 are collected. Said signals are indicative for the sensed wavefront characteristics.

n step S13, the collected signals are processed for obtaining said transient event parameters. For example, said processing may be executed by a central processing unit of the distribution network 10. As indicated above, method step S20 of Fig. 6 includes steps S20a - S20c :

In step S20a, a model for modeling a hazard in the distribution network 10 is provided. Said model is time- dependent and uses a factor vector representing the network parameters, the load-related factors including the transient event parameters, and the external factors.

In step S20b, an actual hazard is modeled by applying determined actual values at least including obtained values of load-related factors including the transient event parameters, the actual values of the network parameters and the actual values of the external factors for the factor vector to the provided model.·

In step S20c, the risk factor is determined in dependence on the modeled actual hazard.

Although the present invention has been described in accordance with preferred embodiments, it is obvious for the person skilled in the art that modifications are possible in all embodiments.

Reference Numerals:

10 distribution network

20 pipes

31, 32, 33 sensor

50 device

51 plurality of sensors

52 determining unit

53 executing unit

CO curve for k=0

Cl curve for k=l

C2 curve for k=2

C3 curve for k=3

d distance

k exponent

LI measurement location, position of first sensor L2 measurement location, position of second sensor L3 measurement location, position of third sensor 0 output

PI first path of pressure wave propagation

P2 second path of pressure wave propagation

P3 third path of pressure wave propagation

S10 - S13 method step

S20, S20a, S20b, S20c method step

S21 - S23, S30 method step

VI, V2, V3, V4 curve References :

[1] A. Large et al: "Decision support tools: Review of risk models in drinking water network asset management", Water Utility Journal 10; 45 - 53, 2015

[2] Sinha and Clair: "State-of-the-Technology Review on

Water Pipe Condition, Deterioration and Failure Rate Prediction Models", available in RDDS

[3] "Application of Artificial Neural Networks (ANN) to model the failure of urban water mains", Mathematical and Computer Modeling, vol. 51, issues 9 - 10, May 2010, pages 1170 - 1180

[4] Procedia Engineering, vol. 186, 2017, pages 117 - 126