Hotspot analysis for integrated multi-infrastructure asset management

Urban infrastructure supports the functioning of society, although it is seldom appreciated by the broader public, as long as they provide the services required and expected. However, as time goes on, these vital infrastructures age and eventually deteriorate from use and abuse, necessitating the management of these assets systematically and strategically. Asset management should be seen holistically, considering the utilities' (or municipal) strategy, risk minimization, public and worker safety, environmental impact, and societal factors in addition to the operation and maintenance of an asset (Amadi-Echendu 2004). Asset management is not a novel concept. Rather, it is a developing one that has been the focus of interest for organizations that operate or control various types of infrastructures. Numerous definitions and applications of the phrase ‘asset management’ exist, each with considerable variances. ISO 55000 (2014) defines it as the ‘coordinated activity of an organization to realize value from assets’. Regardless of the context in which the phrase is used, asset management refers to a combination of management, financial, economic, engineering, and other practices applied to physical assets to maximize the value of an asset stock over its whole life cycle, within the context of delivering appropriate levels of service to customers, communities and the environment at an acceptable level of risk (Marlow et al. 2010).

Asset management in the domain of urban infrastructure is a complex undertaking, rife with a myriad of challenges. The challenges span from the aging of assets and restricted maintenance budgets, to increasing facility usage and heightened societal demands for service quality. In a broader context, infrastructure systems and their constituent components function as interconnected, complex, and adaptive systems, meaning that the dynamics in one can have cascading impacts on others. Despite this inherent interconnectedness, existing asset management practices often operate in silos. Each type of infrastructure is typically managed autonomously, and associated data are frequently stored in disparate, incompatible dashboards (Marzouk & Osama 2017). This fragmentation can lead to inefficiencies, difficulties in data sharing and analysis, and hindered collaboration between stakeholders (Okwori et al. 2021). Consequently, a multidisciplinary approach is necessary for the efficient management of physical assets (Kielhauser et al. 2017).

Additionally, urban infrastructures are becoming more linked and dependent on one another as the globe continues to urbanize (Satumtira & Dueñas-Osorio 2010). In the existing body of literature, several studies have advanced methodologies to quantify interdependence, particularly concerning temporal and spatial dimensions. Time-series analysis was used by Dueñas-Osorio & Kwasinski (2012) to examine the degree of interdependence (or ‘coupling strengths’) between infrastructure networks. They examine this strategy by analysing reactions to utility service restoration. Data from individual utility service systems, or lifeline system restoration curves, were obtained using post-disaster restoration information from the 2010 Chilean Earthquake, demonstrating the gradual restoration of electricity, water, and telecommunication services available as a function of time. The restoration data's auto-covariance and autocorrelation were evaluated to assess temporal interdependence within the same system.

The spatial correlation between network components and their performance is another crucial factor in assessing interdependency, particularly for infrastructure networks. As shown by Lee & Kiremidjian (2007), spatial proximity across networks has significant importance for modelling infrastructure interdependencies, particularly in the aftermath of natural catastrophes like earthquakes. Geostatistical approaches, such as ordinary point kriging, may be used in a probabilistic study of infrastructure networks to quantify the interdependencies as distributed in their service area spaces and are useful for modelling spatially dependent systems. Wu et al. (2012) present the use of kriging surfaces on utility restoration data and the computation of spatial correlations to estimate the spatial distribution of network interdependencies among the lifeline systems of their study area. Although both the time-series model and spatial methods provide unique insights into the true nature of interdependent infrastructure networks, novel techniques to estimate and modelling of networks attempt to consider more realistic constraints, such as when both correlations are present in a single spatial-temporal model (Chan & Dueñas-Osorio 2014).

Linear infrastructure systems (e.g., roads, water/sewer/power lines) are often spatially correlated (Mair et al. 2017) and intervention in one system may affect the serviceability of the other system (Marzouk & Osama 2017). As a result, it may be ineffective to use an asset management paradigm that only considers one infrastructure. This inefficiency may be seen directly when calculating the expenses associated with repeated setup, excavation, and backfilling, as well as indirectly by considering the social costs associated with interruptions, traffic delays, and delays due to rehabilitation work (Abu-Samra et al. 2020; Pericault et al. 2023). Theoretically, by collaborating with other utilities, a utility may avoid repeating tasks, and thereby split costs. The concept of integrated multi-infrastructure asset management (IMAM) is based on taking advantage of these synergies (Daulat et al. 2022). Adopting IMAM offers multiple advantages, such as minimizing service disruptions, reducing maintenance costs, and lowering environmental impacts. Importantly, it fosters cross-disciplinary information flow, thereby enhancing the efficiency of managerial decisions.

On a tactical level, the goal of IMAM is to combine the temporal and spatial relations of different network elements to identify locations for multi-infrastructure interventions. The literature in this area is limited but evolving. The literature can be mainly divided by the way they account for geographical vicinity, either by using street sections as containers for the infrastructure below (Inanloo et al. 2016; Tscheikner-Gratl et al. 2016) or by applying some metric of vicinity (e.g., Kielhauser et al. 2017). Some examples are highlighted here, a thorough review of approaches is provided by Daulat et al. (2022).

To facilitate multi-infrastructure interventions (i.e., coordinated interventions of spatially co-located infrastructures) of municipal assets utilizing a GIS platform, Islam & Moselhi (2012) proposed a model for classifying assets systematically based on their geometry and location. In addition, a three-stage paradigm for multi-infrastructure rehabilitation was developed. It included network analysis, asset dependency, and integrated planning. For integrated intervention planning for water, sewage, and road assets, the integrated planning module used a threshold-based computational model. This study is considered one of the first initiatives that provided a detailed spatial analysis that can be utilized as a springboard for data preparation to enable the integration of interventions for co-located assets. Carey & Lueke (2013) explored the economic benefits of coordinated management across multiple types of infrastructure, although their study employed simulated hypothesized rather than real-world data. Similarly, Marzouk & Osama (2015) delved into optimization strategies for timely asset replacements across a range of infrastructures but also did so in a hypothetical setting. To assist in decision-making for municipal infrastructure, Shahata & Zayed (2016) introduced an integrated risk assessment framework that prioritizes rehabilitation projects using mixed Delphi and analytical hierarchy processes paired with unsupervised K-means clustering. Moreover, others investigated multi-objective optimization to model the suitable intervention timing for two or more networks (Abu-Samra et al. 2020). However, due to some limitations (e.g., dataset size, computational cost), few numbers of corridors were compared.

For the temporal relations, deterioration models are the weapon of choice for most studies. Depending on the infrastructure and the time of application, the methods differ. The same is true if the application is on a strategic level (often using network-level models, like Cohort survival) or on a tactical level (preferring pipe-based models, often using machine learning). An example of the strategic level application is the work of Pericault et al. (2023), which used a cohort survival model for water distribution, sewer, and road, and introduced the concept of a coordination window for integrated rehabilitation. On a tactical level, the focus is on the optimization of such rehabilitation activities, be it by using multi-criteria decision analysis (e.g., Tscheikner-Gratl et al. 2016) or multi-objective optimization (e.g., Minaei et al. 2023). As there is still not a lot of practical application of such approaches, Daulat et al. (2022) synthesized seven key challenges that could obstruct the widespread adoption and effectiveness of IMAM – dependencies and interdependencies, data quality, availability and interoperability, uncertainties in modelling and decision-making, comparability, and problems of scale, fit, and interplay. For the problem of interplay, the lack of tools to streamline the coordination between infrastructures was highlighted.

Consequently, the question of how spatio-temporal information models from interdependent infrastructure networks can be integrated and presented on a unified platform to facilitate integrated intervention planning is addressed in this article. The spatial models of infrastructure networks represent the trenches required for open-cut interventions. From the spatial models, the spatial relationships of infrastructure network elements are obtained. These relationships are represented by the extent (percentage) of shared trench area and volume among the infrastructure networks. The temporal models of the infrastructure networks are represented by their deterioration models, which indicate the timing of interventions. Then, the temporal and spatial information of sewer, water, and road networks is combined to identify hotspots for multi-infrastructure interventions within various time frames. This approach must be seen as a link between tactical and operational planning, since it requires a commitment anchored in the strategies of the utilities involved. The hotspots can be utilized as an information and negotiation tool between those utilities rather than an optimization tool. This is a deliberate choice, as the confidence in formulating a sufficiently precise optimization problem in a highly interconnected environment, with manyfold external influences, uncertainties in the used models (e.g., Fugledalen et al. (2021)), and the available data, and multiple stakeholders and viewpoints seems overly ambitious, and may lead to sub-optimal solutions. On the other hand, in multi-criteria decision analysis, the inclusion of decision-maker preferences is often overlooked and done theoretically rather than practically (Tscheikner-Gratl et al. 2019). Therefore, the hotspot analysis shown here is meant to be an information source for the stake-holders rather than an optimal solution.

It should be highlighted that this study is a proof of concept using only the three most prevalent infrastructures in a real-world case study: water supply, sewer and stormwater, and roads. These were selected for the representability of linear infrastructures. However, the approach could be expanded to include other similar infrastructures (e.g., district heating, electricity, gas, etc.) as well as more spatially confined ones, such as wet-weather control practices (e.g., green infrastructure, structures, etc.) if the necessary data for the spatial and temporal models are available. It should be noted that while data for developing spatial models for wet-weather control practices are usually available (e.g., see Todeschini et al. 2018), data for developing the temporal models can be rarely found (see Bahrami et al. (2024) for green infrastructures). Hence, the expansion of the work can be limited by the unavailability of data.

The spatial model uses the layout of the infrastructure networks (depicted through lines), together with their design and construction guidelines, to estimate their zone of influence described by the necessary surface area and excavation cubature for open trench interventions. The spatial model is also used as a proxy to define and quantify the degree of co-location between infrastructures. The degree of co-location is quantified by quantifying the shared trench volumes and surface areas between multi-infrastructure assets. Higher shared volumes/surface areas mean a higher degree of co-location and a higher potential for cost-saving, but also pose a higher risk of disruption to road, bike lane, and pedestrian services. Generally, the needed inputs should be readily available from the utility organizations managing the respective infrastructures. The methods used to achieve the spatial model of trenches and the degree of co-location is described in Daulat et al. (2024a).

The spatial model is fully implemented using Python scripts and relies primarily on two libraries for its operations. First, GeoPandas (Jordahl et al. 2023) is employed for buffering and intersecting simple shapes akin to rectangular prisms. Second, Geometry3D (Gou 2021) is used for handling more complex three-dimensional intersections, such as those involving trapezoidal prism-like trenches. GeoPandas is developed for spatial data management and processing and is built atop the pandas library (McKinney 2010). While Geometry3D can process any convex 3D shapes, it is generally less efficient than GeoPandas. Consequently, Geometry3D is utilized specifically for cases where GeoPandas does not suffice for processing particular trench geometries.

For visualization purposes, the spatial model serves as a two-dimensional representation of the network of trenches required for open-cut interventions on individual infrastructure assets and provides underlying information about trench volumes and overlaps. The output of the model is a polygonal representation of the trench surface areas for each infrastructure network. Roads are an exception. Their surface area generally suffices as the trench area for interventions, unless deep excavations are necessary due to local soil conditions, in which case, trench dimensions may need adjustments for safety considerations.

The temporal model utilizes deterioration models for each type of infrastructure to estimate the likelihood of failure over time. This allows to gauge when an asset might reach or cross a predetermined threshold, signalling the need for intervention. In this regard, any probabilistic or machine learning model capable of predicting the likelihood of failure (see Barton et al. 2022) can be utilized. To model the deterioration of the sewer pipes and the water distribution pipes, a random survival forest (RSF) (Ishwaran et al. 2008) algorithm was chosen due to its ability to model the survival probability of assets over time and its superior performance compared with other popular models. Daulat et al. (2024b) used it to model water pipe breaks in Norway, showing a reasonable performance of the model. Snider & McBean (2021) showed the superior performance of RSF by comparing it with a statistical model and the popular random forest model (Breiman 2001). Similar results could be seen for sewers in the study of Laakso et al. (2019). Moreover, in RSF, unlike traditional statistical models, various factors that contribute to asset degradation can be easily incorporated, including material type, age, history, and other relevant factors.

Here, X represents the input variable j for individual i; y denotes the split criterion for input variable j; I is the indicator function, which equals 1 if X is less than y and 0 otherwise; δ_i indicates whether an event is censored; and S(t_i) refers to the survival curve.

Here, t_i represents the time at which at least one event took place, d_i is the count of events that occurred at time t_i, and n_i indicates the number of pipes that are known to have lasted up until time t_i.

The survival function for each individual asset is then calculated from the average of the survival functions derived from all trees in the ensemble. If CHF is calculated as the survival function, survival probabilities are then derived from the CHF by the given formula: ⁠, where H(t) is the cumulative hazard function at time t.

The temporal model was fully implemented using Python scripts. The RSF model utilized the scikit-survival library (Pölsterl 2020), using the default parameters provided in the library. Scikit-survival is an extension of scikit-learn (Pedregosa et al. 2011), specifically adapted for survival analysis, yet it retains the robust functionality of scikit-learn.

The methodology for constructing a deterioration model followed a structured, multi-step process that closely adheres to the steps provided in Daulat et al. (2024b) for water and sewer pipes. Initially, data gathering is conducted to collect information on factors that influence asset deterioration. This data is then cleaned and prepared to ensure its suitability for the modelling phase. After data preparation, RSF is then trained using the cleaned and formatted data. After the training phase, the model undergoes a rigorous evaluation to ascertain whether its performance metrics meet an acceptable accuracy. Finally, the trained model is used to predict the future state and performance of water and sewer pipes. RSF may also be suitable for modelling road deterioration; however, since a road model was already available from the municipality, developing another was deemed unnecessary.

The combination of the spatial and temporal models results in a spatio-temporal footprint for each assessed infrastructure. The spatio-temporal models represent a trench surface area network of assets and contain predictions of assets' future performance as their attributes. Once the spatio-temporal models of individual infrastructures are ready, one can select those assets that cross (or have already crossed) a predefined threshold of acceptable probability of failure (or probability of survival), which is called the intervention threshold hereafter, at the year of interest. Then overlay the layers of the models of different networks.

An intervention threshold function must be defined by the individual infrastructure managers and can also vary from asset to asset, depending primarily on the asset's importance. Due to the uncertainties inherent in deterioration models (Fugledalen et al. 2021), fixed and absolute thresholds may hinder the adoption of integrated interventions. It is possible to set a threshold that allows for some flexibility by defining a threshold area bounded by desired and absolute thresholds, as demonstrated in Daulat et al. (2022). Using a fuzzy logic approach, instead of thresholds, is also a possibility. For example, Roghani et al. (2024) used such an approach to estimate the likelihood of failures and consequences of failures in sewer systems. The possibilities can be manyfold but are in the end limited by understandability and usefulness for the decision-makers and should therefore be decided in close collaboration with them. An important aspect should be the consideration of interdependency of infrastructures, as the failure of one asset may affect assets of other interdependent infrastructures. Therefore, the importance of assets, when viewed from the perspective of individual infrastructures, might not always be the same if the interdependencies are considered (Daulat et al. 2022).

After the selection of the assets of interest by the threshold functions, they are overlayed spatially. The result is a new layer that highlights a space from multiple infrastructures, sharing intervention space and crossing their survival probability threshold in the same observation window. Therefore, these assets are deemed suitable candidates for integrated intervention within the specified year. It is important to elaborate on the mechanics of this intersection operation. Initially, the operation occurs between two mutually exclusive infrastructure networks – typically sewer and water systems. To expand this to a third infrastructure type – say, roads – the already intersected layer (between sewer and water) is further intersected with the road layer. This process can be extrapolated to include additional types of infrastructure such as gas and electricity networks by repeating the intersection process in a similar manner. Finally, it is worth clarifying the criteria for considering an asset for integrated intervention. Assets are deemed suitable for integrated intervention if their trenches overlap geographically. Assets in geographical proximity, but not close enough that their trenches overlap, are considered spatially unrelated in this context. Consequently, these assets are not deemed to be candidates for integrated intervention. In other words, the absence of trench overlap means that these assets do not represent a ‘hotspot’ in the integrated intervention plans.

The output is a map of areas where two or more infrastructures are likely to require rehabilitation simultaneously. Such a map, when used alongside detailed maps for the individual infrastructures and provided with sufficient planning time, can serve as a basis for discussion and negotiation among the different utilities involved. This can be especially of interest in the interface between strategic and tactical planning. Additional information provided for these negotiations is the attributes of the assets (such as age, material, diameter, and traffic load), the results from the deterioration models (indicating the probability of failure/unacceptable condition), and the outputs from the degree of co-location models (which can be used as indicators for cost-sharing).

For the deterioration modelling of water distribution pipes, the RSF was trained and tested 15 times (as training more than this did not provide significantly different results), each time with a random train–test split. The train sets used 85% of the available data, and the test sets used the remaining 15% of the data. The RSF in this case predicts the probability of a burst occurring in each pipe at a given time. The model performance was evaluated using the concordance index (C-index) (Harrell et al. 1996) and concordance index-inverse probability of censoring weights (C-index-ipcw) (Uno et al. 2011). The metrics measure the goodness of fit of survival models. C-index-ipcw is preferred because it tries to balance the imbalanced proportion of censored and broken pipes. Daulat et al. (2024b) used both metrics to evaluate the performance of RSF models for water pipe break prediction.

For the sewer pipe deterioration modelling, the RSF model was trained using the inspected pipes. These pipes are classified into five distinct condition classes. A condition class of 1 indicates that the pipe is in very good condition, while higher condition classes signify a worsening state. Condition class 5 designates the pipe as being in the poorest condition, necessitating immediate attention. In this study, the two most severe condition classes were aggregated into a ‘bad condition’ group, while condition classes 1–3 were grouped as ‘good condition’. This approach led to the creation of a binary variable for the deterioration model, enabling us to distinguish between pipes needing intervention and those in a relatively satisfactory state. Similar to water pipe deterioration modelling, using 85% of the data, 15 RSF model for sewer pipes were trained and then tested on the remaining 15% of data, each time with a random train–test split. C-index and C-index-ipcw were used to evaluate the model performance. However, in this case, C-index is the preferred metric for model evaluation as the data used for training and testing contains only the inspected pipes, that is, uninspected pipes are not included in the training and testing.

The reason behind excluding uninspected sewer pipes but including censored water pipe breaks lies in their operation behaviour and data collection mechanism. In principle, a water pipe break is recorded but a sewer pipe's condition is assessed mainly when inspected, unless a severe consequence is noticed due to its break. Accordingly, there is censored break data (break not occurred yet) in water pipes, but there are no censored condition data (condition not changed yet) for sewer pipes.

For road deterioration, an existing model (GSA SWECO 2021) of the municipality was used that provides a proposed rehabilitation year as output. Roads are divided into homogeneous sections based on their condition, layout and traffic load groups. The road network is assessed for 11 types of damage, which will then result in a residual utilization time. The programme uses separate projection models for each type of damage.

To demonstrate the applicability of the proposed method, the thresholds for interventions used are the road's predicted rehabilitation year obtained from the model. For the piped networks, a threshold function (survival probability = 50%) was used. To explore the impact of a more flexible intervention threshold, we tested different buffer times, aligned with the coordination window of Pericault et al. (2023). This involved including assets that are within 2, 5, or 10 years of reaching these thresholds. The aim was to demonstrate how varying buffer times can influence planning decisions in both tactical and strategic contexts.

For spatial modelling, water and sewer networks, represented as polylines, were buffered (Jordahl et al. 2023) to obtain the assets' trench network in polygons. The buffering width was calculated based on the recommendations by Norsk Vann (2004) for trench shapes and dimensions, which states if the trench depth (which in turn is based on pipe depth) is more than 2 m deep, the trench should be excavated in a trapezoidal shape with 45-degree slope on the sides otherwise rectangular shapes with 90-degree slopes can be considered. Most of the water and sewer trench networks of the study area fall into the category of trapezoidal shape as their depths are more than 2 m deep (based on the guidelines from Norsk Vann (2004)) and a few in the category of rectangular shapes. The road networks, also presented by polylines, were buffered by the width of the actual roads as trenches for roads are normally excavated in rectangular shapes as their depths are normally less than 1 m.

After buffering to represent the trench surface areas, a clipping function from the GeoPandas library (Jordahl et al. 2023) was used to highlight and calculate the proportion of intersected areas among the trenches of different assets. For calculating the volumetric intersection among the rectangular prism-shaped trenches, the intersected surface area was multiplied by the depth of the shallowest trench. For trapezoidal prism-shaped trenches, the trench coordinates were provided to the Geometry3D library (Gou 2021) to construct a three-dimensional model of the trenches, and then the intersection function of the library was used to calculate the intersected volumes.

The spatial model shows that in the case study area the road trench network shares approximately 44% of its surface area with both water and sewer trench networks. When considering the road with water and sewer networks separately, it has shared surface areas of 28 and 34%, respectively. From the side, about 28% of its trench network's surface area is shared with both road and water trench networks. Exclusively, the sewer shares 21 and 25% of its surface area with the road and water, respectively. The water trench network, showing the highest degree of surface area co-location, shares roughly 48% of its surface area with both the road and sewer trench networks. Interestingly, the addition of the road network does not increase the shared surface area of the water trench network with sewers, which stands at about 48%. However, the water network shares 35% of its surface area exclusively with the road network. In terms of volume sharing, the water trench network shares 58 and 19% of its volume with the sewer and road networks, respectively. The sewer networks share 24 and 8% of their trench volume with water and road networks, respectively. Last, the road networks exhibit a 26 and 29% volume sharing with the water and sewer networks, respectively.

Figure 4(a), for example, shows that when using the map today as a forecast to 2030, several areas could be of high interest for collaboration between all three infrastructures and between each two mutually exclusive infrastructures. The count of overlapping areas (spatio-temporal intersections) among sewer, water, and road segments up to 2030 is 986.

The areas of potential collaboration increase even further when flexibility in the timing of interventions is added (Figure 4(b)–4(d)). When a 2-year buffer was introduced (Figure 4(b)), considering interventions for assets that cross the threshold line by 2032 as eligible for 2030, the intersection count increased to 1,094. Extending the buffer to 5 and 10 years (shown in Figure 4(c) and 4(d)), the intersection counts further increased to 1,348 and 1,667, respectively. This is also in line with the optimal coordination window of 25 years found by Pericault et al. (2023). Such a map, with the information layers for each of the areas, can be an invaluable discussion frame for rehabilitation planning.

Figure 5 shows the opposite – a very short-term outlook. The utilities in 2029 prepare a plan for the year 2030. It shows that such a short planning window (or coordination window) is not very suitable for integrated interventions as it hampers the flexibility of the utilities. For example, in the no buffer time scenario (Figure 5(a)), only five areas could be of interest for collaboration, one between water and road, and four between sewer and road. The areas of potential collaboration can increase when flexibility in the timing of interventions is added (Figure 5(b)–5(d)). When a 2-year buffer is introduced (Figure 5(b)), the intersection count among sewer, water, and road segments increases to 3 (from 0) corridors. Extending the buffer to 5 and 10 years (shown in Figure 5(c) and 5(d)) further increases these intersections to 18 and 58, respectively. It also shows that if IMAM should be successful, a mere information platform for rehabilitation projects in the near future may not be sufficient. Rather incentives (e.g., in regulations or by funding mechanisms) for regular discussions using visualizations like the hotspot maps should be given.

Introducing flexibility in intervention planning allows for the consideration of uncertainties associated with predicting future asset performance (Esders et al. 2015; Zuluaga & Sánchez-Silva 2020). Although increased flexibility in intervention timing can lead to more potential collaboration areas, utilities are constrained in implementing such flexibility. This is because the number of projects a utility can manage at any given time is limited by resources such as budget, manpower, and machinery. The extent of flexibility is also influenced by the results of deterioration models, their associated uncertainties, and the importance of assets. In this municipality, the deterioration model for roads is updated every 2–3 years for high-traffic roads and every 5 years for low-traffic roads, as the model's reliability diminishes over longer periods. Therefore, in this case, adding flexibility beyond 5 years in projects where roads are involved may not be practical.

The map can also serve as a preliminary tool for deciding the implementation of trenchless technologies, which greatly reduce the need for digging. Areas without hotspots indicate locations where such technologies are particularly suitable as integrated interventions are not possible or advantageous. Also, the hotspots between the sewer and water, where road is not highlighted, can be an option for trenchless technologies (Jung & Sinha 2007). Trenchless methods typically offer a more economical and faster alternative to traditional open-cut methods, while also minimizing disruptions to traffic and communities as well as the environmental impact (Jung & Sinha 2007; Zhu et al. 2021). Consequently, wherever feasible, trenchless solutions are favoured, eliminating the necessity for trench excavation.

In this example (see Table 2), it is not allowed to show real data due to data security concerns of the municipality as a real-world example, but rather an anonymized one with hypothetical data and an exemplary reasoning provided for a qualitative data quality assessment, which of course needs to be done on a case-by-case basis. In this case, a road section, two different water distribution sections, and a sewer section are included.

What is of importance for an informed decision depends on the stakeholder preference, as well as data availability and data security concerns, and should be decided beforehand by the utilities involved. The base data of the infrastructure involved shown here is based on minimal data requirements defined by Tscheikner-Gratl (2016) and is not exhaustive. This includes the construction years (and in consequence infrastructure age) and material information. The base data, depending on the availability, quality, and information needs, can be extended. Data quality is, by definition, a user-dependent criterion, as high-quality data is the data fit for use by data consumers (Strong et al. 1997). It, therefore, needs to be defined by the stakeholders. One can follow for example a structured approach using usefulness as main objective (similar to Pedersen et al. (2022) for models) or the four data quality categories (intrinsic, accessible, contextual, and representational) defined by Strong et al. (1997). We decided in Table 2 to use accessibility, described by source availability, and intrinsic data quality, described by the possibility and effort necessary for data validation. Consequently, those categories are translated into an easy to grasp traffic light colour-coding in Table 2, with red marking low quality and green high quality. Missing data is also highlighted (in our case blue). The reasoning in the following paragraph is case study dependent and needs updating for each case as well as over time to be useful.

Regarding the construction year of the studied networks, it is almost impossible to check if the construction years before 1945 are in fact correct, and validation of construction years until 2000 usually requires checking archival paper plans. This extends to other information on network qualities such as material and diameter, that can be crosschecked for plausibility, but are difficult to control in practice, except if inspection is possible or carried out in recent years (as in this example for the sewer). Another important piece of information is also when the last inspection (visual, or measurements) was made and what the results were. Visual inspections have always been an inherent subjectivity and are therefore less reliable than the measurement of structural parameters (e.g., pipe wall thickness). The next information available is the results of temporal models. Usefulness of the model results can be expressed as a function of the uncertainty inherent in the modelling effort, caused by the quality of the data sources, modelling approach selection and prediction window. It has been shown that the uncertainties for sewers in an age range similar to those shown Table 2 are lower (Fugledalen et al. 2021), while for the water distribution pipes in the shown age range is quite high (Daulat et al. 2024b). Furthermore, the overlapping areas and volumes (as explained in Daulat et al. (2024a)) from the spatial models are of interest as they can be used as proxies for cost-sharing potential and zone of influences. As the calculation is based on data in which depth data is approximated, they include high uncertainty when used on a project level. However, they could be easily improved if the necessary data is available. Finally, if a risk-based assessment is wanted, a level of importance of the given infrastructure element is necessary. That can be assessed by different means. Either by measured proxies e.g., for the road using the amount of daily traffic, or by using models, e.g., for sewers estimating the effect of an element failure on pluvial flooding, the service provision or the environment by assessing combined sewer overflows.

In this study, it is assumed that deterioration models are independent. However, the state of each infrastructure can influence the other ones. For example, a failure in the structure of sewer pipe can lead to ground settlement and damage to the road (Roghani et al. 2024). This limitation can be improved once models (and data) are available to account for these processes, which is a general shortcoming of the work at the moment.

To overcome the challenge of silo-based intervention decisions of highly interconnected infrastructure networks, this article combined the temporal and spatial information of sewer, water, and road networks to identify potential areas for integrated interventions. The results of the study, encapsulated in ‘hotspot maps’, offer tactical insights into where multi-infrastructure interventions could be feasible both spatially and temporally. These maps serve as potent tools for decision-makers, offering a wealth of underlying information that could lead to coordinated interventions. To further increase the potential for coordinated interventions, the article proposed adding flexibility in intervention planning. The findings showed that with increased flexibility in intervention decisions, the potential for coordinated interventions also increases. In the case study examined in this study, the introduction of a 5-year intervention flexibility, which deemed to be practical for this case, increased the number of collaborative projects between sewer, water, and roads from 0 to 18. By applying the proposed methodology, utilities can engage in joint planning and coordinated actions, thereby enabling more effective utilization of investments, and reducing the disruption to the community. While the hotspot maps were generated for a specific projection year (2030), it is worth noting that the reliability of these predictions diminishes with an increase in the projection timeline due to inherent uncertainties.

The maps can also be used for identifying potential areas for applying trenchless technologies. That is, areas without hotspots indicate locations where such technologies are particularly suitable. Future work should focus on extending the methodology to operational level (i.e., project level) coordination, and include other types of linear urban infrastructure, like gas and electricity networks, as well as more spatial infrastructure, like stormwater management facilities. The work can also be supplemented by incorporating the effect of failure of the networks on each other. The work provides a step towards the actualization of an integrated approach to managing the increasingly complex web of urban infrastructure systems. However, the study does not offer a framework that makes assumptions about stakeholder behaviour.

We express our gratitude to Associate Professor Jeroen Langeveld for his valuable feedback and engaging discussions. His insightful contributions have significantly enhanced the quality of this manuscript.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.