Assessing Project Resilience Through Reference Class Forecasting and Radial Basis Function Neural Network

Abstract

A project needs to be able to anticipate potential threats, respond effectively to adverse events, and adapt to environmental changes. This overall capability is known as project resilience. In order to make efficient project decisions when the project is subjected to disruption, such as adjusting the project budget, reformulating the work plan, and rationalizing the allocation of resources, it is necessary to quantitatively understand the level of project resilience. Therefore, this paper develops a novel approach for forecasting project performance, illustrating the changes in performance levels during the disruption and recovery phases of a project and thus quantitatively assessing project resilience. While there are several methods for assessing project resilience in existing research, the majority of assessment approaches originate from within projects and are highly subjective, which makes it difficult to objectively reflect the level of project resilience. Moreover, the availability of project samples is limited, which makes it difficult to forecast the level of project performance. In view of the fact that the Reference Class Forecasting (RCF) technique avoids subjectivity and the Radial Basis Function (RBF) neural network is known to be better at forecasting small sample datasets, this paper therefore combines the RCF technique and the RBF neural network to construct a model that forecasts the project performance of the current project after experiencing a disruption, further assessing the level of the project resilience. Specifically, this paper first presents a conceptual model of project resilience assessment; subsequently, an RBF neural network model that takes into account project budget, duration, risk level of disruption, and performance before disruption based on the RCF technique is developed to forecast project performance after experiencing disruption; and finally, the level of project resilience is assessed through calculating the ratio of recovery to loss of project performance. The model is trained and validated using 64 completed construction projects with disruptions as the datasets. The results show that the average relative errors between the forecast results of schedule performance index (SPI) and the real values are less than 5%, and the R² of the training set and the testing set is 0.991 and 0.964, respectively, and the discrepancy between the forecasted and real values of project resilience is less than 10%. These illustrate that the model performs well and is feasible for quantifying the level of project resilience, clarifying its impact on project disruption and recovery situations, and facilitating the decision-makers of the project to make reasonable decisions.

1. Introduction

The construction industry is important for national economics and urbanization. The construction project is often characterized by a long duration, a complicated environment, and a large number of safety risk factors [1]. The internal and external environments in which construction projects operate are becoming increasingly volatile and uncertain due to the frequent occurrence of high-risk events such as financial crises, international conflicts, and natural disasters [2]. During the long-term construction process of a construction project, the complex working environment creates potentially high risks, such as schedule delays (the actual completion date of one or more items of work during the execution of the project is later than the completion date specified in the plan, resulting in an extension of the overall contract period), cost overruns (the financial resources allocated to an enterprise exceed the budgetary limits set for the project), and quality issues (the quality of projects does not meet the specified requirements or expected objectives during the implementation of the project or after it has been put into use). For example, COVID-2019 has led to setbacks in production for most construction companies, and adverse conditions such as material shortages and resource conflicts have led to project cost overruns, delays, and even extended work stoppages [3]. It is now widely acknowledged that this kind of disruption can be a serious impediment to project delivery. To manage the impact of these disruptions, project managers must make decisions such as adjusting the work plan, improving communication and cooperation between parties, and reallocating resources to ensure construction project success [4].

Many studies have been carried out in industry and academia to increase the project’s capabilities in addressing risk or disruption [5]. The industry has developed a number of standards and specifications to guide project risk management practices. For example, the International Organization for Standardization (ISO) has published a series of standards related to risk management, such as ISO 31000 “Risk Management-Principles and Guidelines” [6], which provides a systematic approach to help organizations identify, assess, and respond to a variety of risks, including risks in construction projects. Academics have also conducted a lot of research to explore ways to improve the risk resistance of projects and have proposed various methods and models for risk identification [7,8,9], risk assessment [10], and risk communication [11,12], to help project managers better understand and manage various risks of projects [13]. Against this backdrop, scholars in the field of project management have begun to explore why some projects struggle to survive in the face of adverse circumstances, while others are able to turn the corner. Then, scholars developed the concept of ‘project resilience’ to explain such differences [12]. Resilience originated in ecology, where it was defined as the ability of ecosystems to withstand damage [12]. In the project management field, resilience refers to an individual or a project’s ability to develop and apply its capabilities to withstand adverse disruptions, recover from crises, and anticipate unknown risks [12]. Improving project resilience has become a goal pursued by many construction companies to carry out project practices. Projects with higher resilience can quickly adapt and respond to environmental changes, maintain system stability and continuity, and improve project success and performance.

Besides scholars having introduced the concept of resilience into the field of construction projects, researchers have started to develop a theoretical framework for project resilience, examining its components, influencing factors, and assessment for improvement [14]. However, there is currently no consensus on how to define and assess project resilience [15]. Assessing project resilience is frequently influenced by subjective factors; thus, it is difficult to objectively and robustly reflect the level of project resilience [16]. Additionally, most resilience assessment models are model-driven, with fewer studies focusing on data-driven approaches. Thus, this paper intends to propose a more accurate method to assess project resilience, including developing a quantitative data-driven model and establishing objective resilience assessment criteria. Due to the Reference Class Forecasting (RCF) technique offering an objective approach by considering an external project perspective and the Radial Basis Function (RBF) neural network excelling in fitting nonlinear patterns, especially with small sample sizes, this paper constructs a model by combining the RCF technique and RBF neural networks to forecast project performance, illustrate the changes in performance levels during the disruption and recovery phases of a project, and thus quantitatively assess project resilience. Assessing resilience can provide a theoretical basis for project decision-makers, such as adjusting the work plan, improving communication and cooperation between parties, and reallocating resources to ensure construction project success [4].

To summarize, the goal and objective of this paper are to develop a data-driven approach for assessing project resilience. To this end, this paper combines RCF and RBF to construct a theoretical model that can forecast project performance levels and then assess project resilience on this basis. The proposed model is validated with 64 construction projects to demonstrate its feasibility and applicability. The model in this paper can be effectively used to assess project resilience, serve as a bridge for future research, and provide clear guidance for project management.

The remainder of this paper is organized as follows: The following section provides an overview of resilience definitions, as well as resilience assessment, RCF technique, and RBF neural network applications. Subsequently, based on the RCF technique, an RBF neural network model is established to forecast project performance levels and assess project resilience. Then, the model is validated using 64 construction projects that have faced disruptions from various sources. Finally, we discuss the theoretical contributions and practical implications of this paper.

2. Literature Review

In this paper, the traditional literature review method is employed to identify relevant literature. A search is conducted in Web of Science using the topic item ‘project resilience’ or ‘assessing project resilience’ or ‘resilience assessment’ or ‘quantify resilience’, and the keywords ‘resilience assessment’ or ‘measure resilience’ or ‘quantify resilience’ or ‘RCF technique’ or ‘RBF neural networks’. This retrieved 337 articles. Subsequently, the same method is employed to identify 70 articles on Elsevier Science Direct and 306 articles on Engineering Village. Duplicate articles from the three data sources are removed, and then articles unrelated to construction projects and those with missing information are excluded. The final number of relevant articles obtained is 40, as shown in

Table 1. Number of articles in different journals.

Journal Name	Number of Literature
International Journal of Project Management	5
Reliability Engineering and System Safety	4
European Journal of Operational Research	3
Automation in Construction	2
Buildings	2
Applied Sciences	2
Journal of Management in Engineering	1
International Business Review	1
Sustainability	1
Journal of Construction Engineering and Management	1
Safety Science	1
International Journal of Information Systems and Project Management	1
Decision Support Systems	1
International Journal of Environmental Research and Public Health	1
Annual Review of Ecology, Evolution, and Systematics	1
Journal of Management	1
Journal of International Business Studies	1
Long Range Planning	1
Data and Information Quality	1
Heliyon	1
IEEE Transactions on Neural Networks	1
Neural Computation	1
Information Sciences	1
Archives of Civil And Mechanical Engineering	1
Journal of Civil Engineering and Management	1
Computers and Operations Research	1
Structural safety	1
Fuzzy Sets and systems	1

. In this section, we will discuss the concept of resilience, the assessment of resilience, the RCF technique, and RBF neural network applications in extant literature.

2.1. Definition of Resilience

The concept of resilience was originally derived from the Latin word “resilio”, meaning to return to one’s original state. Initially applied to physics as engineering resilience, the concept was later introduced to ecology by Holling in 1973 [17]. In common definitions, resilience is often viewed as a static capacity or dynamic process that includes the potential ability of a system to anticipate, avoid, and adapt to environmental shocks [18]; the ability of a system to continue functioning in the face of a disruptive shock [19]; or the ability to withstand a shock and to recover from it [20,21].

The concept of resilience has then been widely used in physics, material science, psychology, environmental science, and emergency management [22]. In the field of project management, Geambasu et al. [23] first proposed the concept of project resilience, which is considered to be the ability of a project to withstand and continuously adapt to change. Then, more and more scholars proposed different concepts of project resilience, which can also be generally categorized into two major kinds: process perspective and capability perspective [24].

(1) From a process perspective, project resilience is considered throughout the project and focuses on the long-term development of the project. For example, Wang et al. [25] adopt a process perspective to understand and construct project resilience. They define project resilience as the ability to withstand shocks, cope with challenges, and recover. Turner and Kutsch [26] call for the development of the concept of project resilience and mention that it involves anticipating, understanding change, and planning for scenarios to minimize losses and adapt to new realities.

(2) From a capability perspective, project resilience is often linked to “resistance”, “adaptation”, “rebound”, and “learning” [22]. For example, Blay et al. [27] conceptualize project resilience in their empirical study of engineering projects as the ability to prepare for, respond to, and mitigate the impacts of disruptions to ensure successful project delivery. Zarghami et al. [15] see project resilience as a set of interrelated capabilities that projects need before and after a disruption occurs, and that should be complemented by the development of preparedness capabilities to recover from the disruption before it becomes apparent. The process perspective definition is more applicable when looking at the full life cycle of a project, whereas the capability perspective is more concerned with the state of recovery of a project after it has been subjected to a disruption. The research perspectives used vary depending on the focus of the research.

2.2. Assessing Resilience

The inadequate performance of traditional project risk management has prompted a growing demand for research on project resilience. However, the absence of a unified theoretical framework and assessment methodology has resulted in a limited number of studies adopting the concept of “project resilience” [22], in comparison to those on organizational resilience. Project resilience assessments can be broadly categorized, including subjective and objective approaches [22].

(1) Subjective assessment methods are employed to identify and quantify resilience at the individual and organizational levels [16]. These methods include self-assessment, expert assessment, and group discussion, which provide insights into respondents’ perceptions and assessments of resilience levels, such as the ability to cope with stress and challenges, adaptability, and other aspects [28]. Modeling studies can typically be conducted using techniques such as fuzzy analysis or Bayesian networks [29]. However, studies based on such methods are inherently subjective because they are not based on specific historical data but rather on expert experience. These assessment methods rely excessively on the a priori knowledge of the experts [30], and at the same time, due to the differing experiences of each expert, there is a certain cognitive bias, and the scoring criteria provided are different, which results in a certain degree of bias in the assessment of project resilience.

(2) An objective method of assessing project resilience can be achieved by quantifying various indicators such as resource reserves, emergency response capacity, speed of recovery, and other attribute data and indicators [7]. These indicators are obtained through historical data, statistical analysis, and other means, such as data on project schedule delays, cost overruns, and disaster losses [31]. An indicator system is typically developed around the concept of resilience, followed by a comprehensive assessment using quantitative methods such as entropy weights [32], hierarchical analysis [33], TOPSIS [34], Monte Carlo simulations [35], and fuzzy logic systems [36]. Monte Carlo simulation and fuzzy logic are two different, but both play an important role in dealing with complex and uncertain problems. Furthermore, project resilience assessment may be based on the performance level change curve of a project following a disruption [15]. From this curve, various attributes may be extracted, including the magnitude of the decrease in performance level, the degree of recovery, the length of recovery, the speed of recovery, and the average cumulative consequences, which may be subjected to a specific mathematical operation (e.g., multiplication) [10,32,37]. While these methods provide an accurate assessment of project resilience, they do not provide forecast results of future trends in the project.

2.3. RCF and RBF Neural Network Applications

In the context of investment decisions, the accuracy of forecasts of the cost and schedule of a project is of great importance. In construction projects, techniques such as BIM (Building Information Modeling) and RCF (Reference Class Forecasting) are often employed in order to forecast project costs and schedules [38]. However, it should be noted that BIM can forecast project costs and schedules [39], but that it relies on the subjective judgment of the project manager, which can lead to cognitive bias. Consequently, Servranckx [38] uses the external perspective—also known as the RBF technique—which was demonstrated to possess a high degree of accuracy in the forecasted results of project costs. Flyvbjerg [40] provides an illustrative example of RCF in practice; that approach was utilized to forecast the costs associated with the Edinburgh Tram. Batselier and Vanhoucke [41] conducted an empirical evaluation of the method by applying it to a dataset comprising twenty-four real-world projects originating from the construction industry. Their findings indicated that the RCF technique is more accurate than traditional forecasting methods and provides more precise forecasts. Consequently, RCF techniques are now being employed in a multitude of contexts, including planning, project management, cost estimation, and strategic management [42].

RBF (Radial Basis Function) neural network is a frequently used model in artificial neural networks [43]. Moody and Darken [44] were the first to try to introduce the principle of RBF function in the design of artificial neural networks, which eventually constituted the RBF neural network. A RBF neural network is composed of an input layer, a hidden layer, and an output layer. The activation function of the hidden layer uses the radial basis function, which weights the input by radial symmetry with the center in the input space to obtain the output of the hidden layer neurons [45]. The radial basis function is known for its strong nonlinear fitting ability and its ability to capture complex nonlinear relationships. As a result, the RBF neural network is highly adaptable when it comes to dealing with nonlinear problems. Although Monte Carlo simulation and fuzzy logic also offer significant advantages when dealing with complex and uncertain problems, they each have some drawbacks. Monte Carlo simulation requires a large number of random samples for simulation and is computationally slow [35]. Fuzzy logic, on the other hand, lacks adaptive and self-learning capabilities, which means that they may not adapt well to environmental changes or the emergence of new data [36]. Meanwhile, RBF neural networks are particularly effective when trained on small sample datasets, as they can achieve better generalization performance with less data. In the event that the quantity of data are considerable in size or the data characteristics are more intricate and diverse, the RBF model may be more susceptible to overfitting as a consequence of the complexity of the data distribution. Additionally, its strong generalization ability means that the performance on the training set tends to translate well to the testing set, allowing for more accurate forecasted results when dealing with unknown data. There have been many scholars applying RBF in different fields, such as construction estimation, schedule forecast, and the daily schedule completion rate of construction projects [46]. For example, Li et al. [47] used neural networks to help tunnel engineers estimate the productivity of the next cycle, thus improving productivity. Lesniak and Juszczyk [48] identified the project type, project geographic location, and duration as the key influencing factors and used neural networks to forecast the project overhead costs.

2.4. Research Gap

The pursuit of greater project resilience has become a key objective for projects. Projects with high resilience are able to adapt and respond rapidly to environmental changes, maintain system stability and continuity, and thereby enhance the success rate and performance level of the project. This, in turn, provides decision-makers with the information they require to make informed decisions. In the current highly competitive market environment, assessing and enhancing construction project resilience has become one of the important means for construction enterprises to obtain competitive advantages in the market. However, due to the lack of a unified theoretical framework and practical path, the connotation and measurement of project resilience are not uniform. Furthermore, only a relatively small number of studies have assessed project resilience, and existing project resilience metrics are often influenced by subjective factors, making it difficult to objectively reflect the level of project resilience. And most of the existing resilience assessment models are model-driven, with fewer studies on data-driven.

To address this research gap, this paper defines project resilience, combines the RCF technique and RBF neural network to construct a model that forecasts the project performance level, and then assesses the level of project resilience by calculating the ratio of recovery to loss of project performance, with a view to providing assistance to project decision makers.

3. Research Design

To address the research questions, a framework was developed, which is realized by implementing a three-step research design (as shown in Figure 1). Initially, a conceptual model for project resilience assessment is constructed in order to develop an account of the project resilience concept, assessment method, and evaluation metrics associated with project resilience. This is followed by the construction of an RBF neural network model based on RCF, which is used to forecast the performance level of the project that will encounter disruption. Finally, the paper uses an assessment of project resilience in order to assess the project resilience.

3.1. Conceptual Model for Project Resilience Assessment

3.1.1. The Concept of Project Resilience

The definitions of project resilience adopted are different due to the different focuses of different studies [49]. In the process perspective, project resilience is defined as the capacity of a project to withstand and recover from disruptions. This can also be considered a form of dynamic resilience. In this perspective, project resilience is viewed as a dynamic developmental process that includes the ability to prepare beforehand, the ability to react during the event, and the ability to recover after the event. A comprehensive assessment of the three phases of capability constitutes an assessment of project resilience.

In the capability perspective, project resilience is defined as the internal strengths and advantageous resources of the project, also known as static resilience. This perspective emphasizes the adaptability and resilience of the project itself and how these capabilities can be effectively utilized to maintain the stability and functionality of the project. It focuses more on the recovery result of the project, as the project itself has certain resilience capabilities that help the project restore its performance after a disruption. Therefore, assessing resilience from a capacity perspective can be assessed using performance indicators from the recovery phase.

This paper also addresses the recovery phase and therefore employs the capability perspective to assess project resilience. In the capability perspective, project resilience is often defined as the capacity of a project to prepare for, cope with, and mitigate the effects of disruptions in order to ensure successful project delivery. Building on this definition, this paper proposes that project resilience is the capacity to enable a project to proactively adapt and maintain its functionality throughout its response to disruption.

3.1.2. Project Performance Indicators

In the field of construction projects, project performance, project management performance, project success, and project management success are all forms of performance-related descriptions in research. The concept of project success is open to interpretation, leading to the conclusion that there is no uniform definition or assessment of construction project performance. Rather, it is based on the overall degree of achievement of construction project goals and expectations. This paper therefore considers that project performance reflects the behavior and outcomes involved in all activities throughout the life cycle of the project and is committed to the achievement of construction project functions.

The concept of construction project performance is multifaceted and intricate. The evaluation of construction projects typically encompasses three key indicators: cost, schedule, and quality, collectively referred to as the “iron triangle” of project performance. In light of this, as well as the gathered project data, this paper selects the schedule performance indicators (SPI) for assessment and analysis. There will be three types of situations:

Type 1: when SPI > 1, it indicates that the progress is ahead of schedule or that the actual progress is faster than the planned progress.

Type 2: when SPI < 1, it signifies that the progress is delayed or that the actual progress is slower than the planned progress.

Type 3: when SPI = 1, it implies that the current progress is consistent with the planned progress.

This paper collates data, conducts analysis and calculates SPI, and presents an associated assessment, thereby enabling an intuitive reflection of the level of project resilience.

3.1.3. Project Resilience Curves

In order to establish a conceptual model for resilience assessment, the following analyses the project’s response process to disruption and the changes in its performance level and specifies the characteristics of the associated resilience capabilities. In particular, the performance level of the system can be assessed from different perspectives and using different indicators, and different performance metrics correspond to different dimensions of the project’s resilience. Different performance indicators can be selected to characterize the different performance levels of the project, such as the progress level of the project, which can be selected as an SPI. Recording the performance level of the project at time t as PI(t), as shown in Figure 2, the performance level of the project changes after the disturbance in four stages as shown below:

Initial stage (t < t₁): the normal operation phase of the project before it encounters a sudden event. In this phase, the project’s performance level P(t) remains at the initial level PI_O.

Disruption stage (t₁ ≤ t ≤ t₂): In the event of a disruption occurring at the beginning of t₁, it can be assumed that the project will be damaged and destroyed solely at that moment. Concurrently, as the project is a temporary organization, the consequences of the catastrophic event will gradually spread throughout the project to the entire organization, ultimately resulting in certain consequences of the disaster. This can be exemplified by the performance level of the network at moment t₁, P(t), which declines from PI_O to a certain value. The decline curve of the project performance level in this phase portrays the project’s ability to resist and recover from the disruption. If the project has not initiated the restoration process by the end of the decline in P(t) at t₂, the project will reach the minimum performance level PI_D1 at time t₂.

Recovery stage (t₂ < t ≤ t₃): During this phase, the project initiates a process of gradual recovery, with the objective of restoring the project performance level P(t) to its original state. This may entail a number of adjustments, including resource reallocation, process optimization, or the activation of contingency plans. In order to accelerate the recovery process, the project may increase its resources, which can be divided into two categories: expendable resources (e.g., money, replacement facilities, and equipment, etc.) and non-expendable resources (e.g., tools, personnel, etc.). The evolution curve of the project’s performance level during the phase is determined by the recovery resources owned by the project and the proposed recovery strategy or plan, in conjunction with the aforementioned resources. The investment of these resources facilitates the prompt resolution of legacy issues and the enhancement of operational efficiency. Following a period of adaptation and adjustment, the performance level of the project gradually stabilizes at t₃.

Stable stage (t > t₃): After going through the disaster recovery phase, the project will be in a new stable operation phase. In this phase, the level of project performance recovery depends on its own recovery capability as well as its recovery strategy and can exhibit three different types of recovery:

Situation 1: The system recovers to the original performance level PI_O;

Situation 2: The system recovers to a higher level of performance PI_R1;

and Situation 3: The system produces a partial loss of performance up to PI_R2.

3.2. Forecasting Project Performance Based on RCF and RBF

3.2.1. Reference Class Forecasting Technique

This paper presents an RBF neural network model based on the RCF technique to accurately assess the level of project performance subjected to a disruptive event. Specifically, we use a combination of RCF and RBF neural networks to construct the assessment mode. In the implementation of the model, we use the RCF technique as the core framework to incorporate external perspectives.

To achieve this, an appropriate reference class must be selected, consisting of historical events similar to the current event to be forecasted. An extensive collection of historical data relevant to the forecasting objective should cover the outcomes and influencing factors of similar projects in the past. The following step involves extracting features from the reference class, which may include factors such as cost, schedule, and risk related to the forecasted event. The purpose of feature extraction is to establish a correlation between the reference class and the forecasted event. The occurrence of the current event is predicted through the established forecasting model. Ultimately, forecasts are generated using the validated model. It is also necessary to compare the predictions with the actual results in order to verify the accuracy of the model and to adjust and optimize it as needed. It should be noted that the effectiveness of the RCF technique depends on the accuracy and completeness of the historical data, as well as on the extent to which changes in the external environment affect project results. Therefore, these factors should be fully considered when applying the RCF technique, and corresponding measures should be taken to improve the accuracy and reliability of the forecast.

3.2.2. Determine Input and Output Variables

Input Variable

Project performance is generally forecasted by Earned Value Management (EVM) methods, which can be used to comprehensively examine project schedule and cost performance.

In this paper, we focus on schedule-related indicators, including Planned Value (PV), Earned Value (EV), Schedule Variation (SV), and Schedule Performance Indicator (SPI), all of which can reflect the difference between the actual schedule and the planned schedule, but SPI is more conducive to the training of the neural network model compared with SV, and is therefore chosen as an input variable. Variables that are closely related to project performance also include the project’s planned duration (PD) and budget at completion (BAC).

Since this paper investigates the impact of project resilience on the disruption and recovery of project performance metrics after the disruption, the input variables also need to consider the level of disruption encountered by the project. In this paper, the risk level (RL) of disruption is scored based on the impact on project objectives, schedule, cost, or quality caused by the occurrence of the risk event. Risk events with a minor impact on project objectives, schedule, cost, or quality can be resolved through the efforts of the project team or simple adjustments, with scores ranging from 1 to 3. Risk events that have a moderate impact on project objectives, schedule, cost, or quality require specific countermeasures, with a score range of 4–7. A risk event can have a significant impact on project objectives, schedule, cost, or quality and may require urgent assessment or re-planning of the project program to address it. The severity of the risk is rated on a scale of 8–10. Finally, the data are processed, with a score range of 0–1. Standardized score values help to harmonize metrics. In risk management, different risk events may have different levels of impact and probability of occurrence, and these values may span a wide range. By standardizing the score values to a range of 0–1, it is possible to use the same metrics for all risk events, thus facilitating subsequent calculations. Meanwhile, in this paper, maximum-minimum normalization is used to linearly transform the original values to the range of 0–1. (maximum-minimum normalization: X_norm = (X − X_min)/(X_max − X_min), X_norm is the normalized value, and X, X_min, and X_max are the original values, the minimum value in the original data, and the maximum value in the original data, respectively).

Therefore, SPI, PD, BAC and RL are selected as input indicators for the model, which are calculated as shown in

Table 2. Scores of different risk levels.

Risk Level	Score
Mild risk	1–3
Moderate risk	4–7
Severe risk	8–10

.

Output Variable

In the context of temporal analysis, the project performance indicator at time t₁ is designated as SPI(t₁). Analogously, at time t₂, the performance status of the project is represented by SPI(t₂), and this sequential notation extends to t_n, where SPI(t_n) denotes the performance indicator at that particular time point. This academic paper endeavors to construct a causal model that incorporates identical variables in both its input and output configurations, albeit across diverse temporal frameworks. Central to this model are the output variables SPI(t₂) and SPI(t₃), which serve as quantitative metrics for assessing the project’s performance across various time intervals. The output variables are shown in

Table 3. Input variable and output variable.

Type of Variable	Variable	Calculation or Description
input variable	BAC	Budget at completion
	PD	Planned duration
	SPI(t1)	EV/PV
	RL	range of values [0, 1]
output variable	SPI(t2)	--
	SPI(t3)	--

.

3.2.3. Constructing RBF Neural Network

The project performance forecasting model designed in this paper uses RBF neural networks to mimic the information processing ability of biological nerve cells and takes the PD, PC, SPI(t₁), and RL of similar historical projects as input variables for simulation during construction projects so as to make a reasonable and scientific change of the current project’s performance indicators.

RBF neural network generally has three layers: input layer, hidden layer, and output layer. As illustrated in Figure 3, the input layer includes four indicators of input: BAC, PD, SPI(t₁), and RL. The number of neurons in the hidden layer is determined by the number of sample items. Finally, the output layer includes two indicators SPI(t₂) and SPI(t₃).

The model training needs to go through a preliminary process first, by normalizing the data. Then, the center vector and normalization constants of the Gaussian function are derived based on the positional division of the data. Finally, after the weights and hidden layer parameters are determined in the learning phase, the weight matrix of the output layer is derived using recursive least squares. The output function is shown in Equation (1):

$$Y={{\displaystyle \sum }}_{i=1}^m{\epsilon }_{i}f\left(x_i-c_i\right)$$

(1)

where Y is the values of the output variables, x_i is i-th input variable, c_i is the i-th center of the function, m is the number of variables, f(x_i − c_i) is the i-th basis function, ε_i is the i-th weights of the nodes of the implicit layer to the output layer.

The basis function is generally a Gaussian function because the Gaussian function has the advantages of rotational symmetry, utility, and simplicity of form. The general expression of the Gaussian function is shown in Equation (2):

$$f\left(x_i-c_i\right)=e^{-{\displaystyle \frac{1}{2{\sigma }^2}}{║x_i-c_i║}^2}$$

(2)

║x_i − c_i║² is edclideannorm, σ is variance of Gaussian function.

3.2.4. Forecasting Performance Indicators

In the constructed RBF neural network model, the data set is reasonably divided into training set and testing set. Use the training data to train the network, and adjust the network parameters to make the output gradually close to the real performance index value. At the same time, the error changes during the train process are monitored. After the training is completed, the test set data are input into the trained RBF neural network to obtain the forecast values of the performance indicators. And compare the forecast values with the real values. Based on the coefficient of determination R² or other performance indicators in order to assess the forecast performance. Based on the evaluation results, it may be necessary to adjust the model parameters and retrain the model until a satisfactory forecast result is achieved. Throughout the process, attention also needs to be paid to the generalization ability of the model to ensure the accuracy and reliability of the forecast results.

3.3. Assessing Project Resilience

This paper defines project resilience from a capability perspective and focuses more on the recovery effects of the recovery phase of the project. Furthermore, project resilience assessment may be based on the performance level change curve of a project following a disruption. This paper refers to existing assessments of resilience indicators such as the sum of project reliability and the degree of recovery after a disruption, the ratio of project performance level recovery at a certain point to the maximum decrease in performance level, and the joint probability of project performance level remaining above a certain threshold after a disruption and recovery time not exceeding a certain limit. Consequently, following the determination of the model parameters, this paper will utilize a range of performance indicators during the interruption and recovery stages to assess project resilience, employing the ratio of project performance degradation to recovery as the assessment method. The specific formula is as follows:

$$\phi ={\displaystyle \frac{\mathrm{PI}\left({\mathrm{t}}_3\right)-\mathrm{PI}\left({\mathrm{t}}_2\right)}{\mathrm{PI}\left({\mathrm{t}}_1\right)-\mathrm{PI}\left({\mathrm{t}}_2\right)}}$$

(3)

Depending on the value of φ, it can be categorized into the following three cases: When φ > 1, it means that the project is more resilient and can recover to a higher level of performance than before; when φ < 1, it means that the project has a lower level of performance and has incurred a loss of performance in the process; and when φ = 1, it means that the project has just recovered to the initial level of performance.

4. Model Validation

4.1. Sample Data for Projects

In this section, we validate the accuracy of the proposed model using historical project datasets derived from the Batselier and Vanhoucke and Martens and Vanhoucke databases. These datasets can be accessed from the official website of the Operations Research and Scheduling (OR&S) research group at the Faculty of Economics and Business Administration of Ghent University (https://www.projectmanagement.ugent.be, accessed on 13 August 2024). The collection of project data started in 2008 and encompasses five major industries: construction, IT, education, production, and finance, and the dataset has been updated to 181 empirical projects in 2023 (

Table 4. Summary of the project dataset.

Sector	Number of Projects	BAC (Min)	BAC (Max)	PD (Min)	PD (Max)	RC (Min)	RC (Max)	RD (Min)	RD (Max)
Construction	122	22,704	4,999,958,016	7	1796	25,313	5,033,780,194	16	1360
Engineering	11	114,700	13,812,919	93	671	190,267	10,687,800	146	673
Mobility	6	396,760	5,611,571	214	400	415,032	5,694,790	350	590
Event management	13	1210	1,287,700	19	148	1780	1,245,022	15	185
IT	27	4020	4,899,912	43	725	3240	1,425,156	37	740
Education	2	43,170	185,472	32	229	83,712	204,739	48	260
Selected Sample data	64	22,704	62,385,600	50	850	25,313	65,526,930	79	935

). The dataset contains baseline scheduling data, risk analysis data, and project control data. These projects came from a variety of countries and regions, with the most expensive project costing €4,999,958,016 and the least expensive costing only €1210. The duration of the projects ranged from 7 to 1796 days. Information about the 181 projects is detailed in Table 3, which contains information about the project type, the planned duration (PD) of the project, the budget at completion (BAC) of the project, as well as the real cost (RC), and the real duration (RD) of the project. Meanwhile, this dataset is frequently adopted by scholars to perform research, such as when Vanhoucke et al. (2016) used the dataset to construct schedules, analyze schedule risks, and perform project control [50]; and Vanhoucke et al. (2018) again used these datasets to conduct a study of scheduling for resource-constrained projects [51].

Instead, this paper focuses on 122 of these construction projects because construction projects are very complex and often carried out in uncontrolled environments where even small disturbances can magnify their negative impacts.

To aid the study, 64 projects are chosen from a portfolio of 122 based on RCF technique and two criteria. First, the project has a complete track record that provided all necessary schedule and cost baselines and project control information. Second, after corrective action was taken, the project bounced back to its original stabilized level or bounced back to a higher level of performance than in the period prior to the disruption. From Table 3, it is clear that out of the 64 items selected, the maximum value of BAC is 62,385,600 and the minimum value is 22,704. Meanwhile, the range of PD is from 50 days to 850 days. The RC takes the range of 25,313 to 655,269,930. And the minimum value of RD is 79 days, and the maximum value is 935 days.

However, due to the limited dataset of the selected project, we expanded the data in order to ensure the accuracy of the experiment. In other words, the number of dataset samples was increased from 64 to 200 through the utilization of interpolation, a process inherent to the RBF neural network. With regard to the expanded sample of 200, we constructed the model by choosing 95% of them as the training set and 5% as the testing set for experimentation.

4.2. Determination of RBF Neural Network Structure and Training Parameters

The RBF neural network is used to train the performance level forecast model of the project, and the function parameters need to be set before training. The mean squared error target of the training structure is GOAL, denoted as α, and its default value is 0; the expansion rate of the radial basis function is Spread, denoted as β, and its size determines the spread speed of the radial basis function. In this paper, the model is constructed by choosing the parameter mean squared error target α = 0.000001 and the spread rate β = 1000.

In this paper, model construction was carried out using a computer of AMD Ryzen 5 5600H with 16 G of RAM, and the model was constructed by MATLAB 2019b. 95% of the sample is used as training samples and the remaining 5% as test samples. Then, build the code as follows: net = newrbe (P_train, T_train, GOAL). Figure 4 illustrates that the greatest training outcomes are attained when GOAL is set to 3. P_train represents the input data matrix of the network, which is typically a matrix where the columns correspond to the distinct training samples and the rows represent the features associated with each sample. T_train denotes the target output (i.e., the desired output) of the network, which is also a matrix. It should possess the same number of columns as the number of samples in P_train, and the number of rows indicates the output dimension associated with each sample.

4.3. Model Result and Analysis

4.3.1. Model Training Results

The neural network is trained in accordance with the specified network structure and training parameters. The resulting model error decline curve and sample data training fit are presented in Figure 4.

As illustrated in Figure 4, the model iteration reaches the fourth iteration when the error reaches the set value of 0.000001. This is indicative of the training data being more accurately represented in the training process, resulting in a more optimal model fit. Consequently, the model training results are more accurate.

4.3.2. Model Forecasting Results

The forecasting error standard value is set at 10%. If the forecast error is less than this value, it indicates that the model’s forecast is reasonable and the model is valid. Inputting the test set into the trained model, the comparison of the forecast and real values of SPI(t₂) and SPI(t₃) are shown in Figure 5 and Figure 6, respectively.

The forecast values of SPI(t₃) and SPI(t₃) as well as the real values for the testing samples are shown in

Table 5. A comparison of the results of the two groups of performance indicators.

Data Packet	SPI(t2)			SPI(t3)
	Real Value	Forecast Value	Relative Error	Real Value	Forecast Value	Relative Error
1	0.7597	0.769	0.0122	1	0.988	0.0120
2	0.7857	0.7895	0.0048	1	0.9785	0.0215
3	0.6711	0.6538	0.0258	1	0.9729	0.0271
4	0.5393	0.5576	0.0339	1	0.9656	0.0344
5	0.6285	0.6385	0.0159	1	0.9645	0.0355
6	0.8425	0.8506	0.0096	1	1.004	0.0040
7	0.7591	0.7695	0.0137	1	0.9818	0.0182
8	0.3844	0.3867	0.0060	1	0.9824	0.0176
9	0.879	0.8824	0.0039	1	0.9904	0.0096
10	0.9881	0.9857	0.0024	1	1.01	0.0100

. As can be seen in Table 5, the relative error between the forecast value and the real value of the test sample data are all less than 5%, which meets the requirement of setting the forecasting error less than 10%. The R² of the SPI(t₂) was 0.99106, and the R² of the SPI(t₃) was 0.96421, indicating that the model fit well after training. By analyzing Figure 6 and Figure 7, it can be concluded that the forecast and real values of SPI(t₂) and SPI(t₃) data values are more in line with each other, thus indicating that the project performance forecasting model established in this paper has a high degree of fit with the actual situation and can accurately assess the level of project resilience.

4.3.3. Statistical Relevance Analysis

In the RBF neural network constructed in the paper, we expand the 64 samples in the dataset to 200 and perform a test. The test result is good. But in order to guarantee the statistical relevance of the conclusions, 100 additional experimental validations of the constructed model are conducted, give the relatively limited data set employed in this study. The statistical relevance of the model is tested by means of a systematic adjustment of the sample size. Specifically, 50% of the total 200 samples are selected as the training samples, and 10 independent randomized experiments are conducted, with R²-values for both the training and testing sets yielded for each. This is conducted in order to assess the reliability of the model. Subsequently, the proportion of the training sample is increased in increments of 5% from 50% to 55%. 10 independent randomized experiments are conducted for each increment, and the results obtained are recorded in

Table 6. 100 groups of comparative experiments.

	Basis for Grouping		R2 of SPI(t2)	R2 of SPI(t3)	Number of Projects with BAC in the Following Ranges (Test) (Unit: €)				Number of Projects with PD in the Following Ranges (Test) (Unit: Days)
	Percentage of Training Sets (%)	Percentage of Testing Sets (%)			[0, 50 w]	(50 w, 100 w]	(100 w, 300 w]	(300 w, 6500 w]	[0, 100]	(100, 200]	(200, 300]	(300, 1000]
1	50	50	0.982	0.969	30	17	31	22	21	26	21	32
2			0.990	0.948	32	20	29	19	22	31	22	25
3			0.991	0.964	25	26	26	23	20	31	21	28
4			0.987	0.986	29	23	34	14	23	29	27	21
5			0.993	0.97	28	23	38	11	18	33	32	17
6			0.989	0.976	26	25	34	15	22	31	23	24
7			0.977	0.991	39	16	31	14	31	25	21	23
8			0.992	0.974	40	18	36	6	34	24	27	15
9			0.988	0.985	27	24	31	18	20	31	23	26
10			0.991	0.951	29	18	35	18	23	24	28	25
11	55	45	0.985	0.988	28	21	34	27	20	30	26	34
12			0.985	0.985	24	30	32	24	17	37	30	26
13			0.987	0.985	40	27	27	16	31	38	20	21
14			0.993	0.957	35	25	32	18	27	33	27	23
15			0.985	0.982	33	20	34	23	23	31	25	31
16			0.988	0.984	31	27	29	23	27	31	22	30
17			0.991	0.979	30	21	33	26	25	27	25	33
18			0.990	0.978	27	24	33	26	22	30	21	37
19			0.985	0.981	29	25	34	22	23	32	27	28
20			0.992	0.958	40	12	35	23	29	24	26	31
21	60	40	0.989	0.979	40	25	33	22	27	39	24	30
22			0.99	0.979	33	31	33	23	25	41	26	28
23			0.988	0.987	40	22	33	25	30	33	25	32
24			0.989	0.985	33	29	25	33	26	37	21	36
25			0.988	0.982	32	26	34	28	25	33	32	30
26			0.989	0.980	33	27	36	24	26	34	28	32
27			0.987	0.986	42	26	29	23	24	44	24	28
28			0.987	0.986	32	33	31	24	25	42	21	32
29			0.991	0.964	26	28	40	26	18	37	28	37
30			0.990	0.981	38	23	36	23	29	33	28	30
31	65	35	0.987	0.988	42	24	36	28	26	40	29	35
32			0.989	0.954	33	30	37	30	29	34	31	36
33			0.996	0.928	39	27	42	22	32	34	36	28
34			0.989	0.983	44	17	30	39	39	23	19	49
35			0.993	0.941	43	29	37	21	36	36	29	29
36			0.984	0.992	35	36	31	28	27	44	24	35
37			0.986	0.985	44	25	34	27	34	35	29	32
38			0.987	0.986	40	26	36	28	29	38	29	34
39			0.989	0.978	36	34	39	21	26	44	27	33
40			0.986	0.988	38	20	38	34	26	34	28	42
41	70	30	0.989	0.980	49	26	42	23	35	43	32	30
42			0.989	0.979	46	27	39	28	32	41	27	40
43			0.987	0.985	45	27	41	27	32	41	24	43
44			0.987	0.988	44	26	48	22	30	41	36	33
45			0.991	0.961	46	29	43	22	37	38	33	32
46			0.988	0.982	46	34	39	21	34	46	30	30
47			0.988	0.985	45	29	40	26	33	43	29	35
48			0.985	0.991	50	25	41	24	35	40	34	31
49			0.987	0.987	47	26	45	22	37	38	38	27
50			0.990	0.970	40	34	36	30	29	47	27	37
51	75	25	0.988	0.984	45	24	54	27	37	34	41	38
52			0.988	0.981	50	34	40	26	38	46	29	37
53			0.987	0.988	43	27	46	34	30	42	34	44
54			0.990	0.965	38	37	44	31	31	44	35	40
55			0.988	0.979	42	36	51	21	30	49	39	32
56			0.986	0.990	51	27	40	32	40	38	30	42
57			0.987	0.984	49	30	36	35	35	44	29	42
58			0.989	0.981	53	35	43	19	41	49	33	27
59			0.986	0.988	47	33	40	30	32	48	32	38
60			0.989	0.980	49	36	36	29	40	46	27	37
61	80	20	0.989	0.978	48	32	47	33	38	43	38	41
62			0.987	0.989	57	33	42	28	41	50	28	41
63			0.987	0.987	57	29	42	32	44	43	33	40
64			0.988	0.985	56	28	43	33	44	40	36	40
65			0.987	0.987	51	31	48	30	39	44	37	40
66			0.988	0.985	53	34	40	33	39	48	33	40
67			0.988	0.984	54	40	39	27	39	55	33	33
68			0.986	0.989	47	31	53	29	38	41	40	41
69			0.988	0.984	41	35	55	29	31	46	40	43
70			0.988	0.985	53	36	46	25	47	43	35	35
71	85	15	0.988	0.97	55	32	54	29	43	45	40	42
72			0.987	0.986	62	36	40	32	42	58	29	41
73			0.987	0.986	47	41	49	33	32	58	40	40
74			0.988	0.980	56	30	48	36	41	46	39	44
75			0.988	0.985	51	38	49	32	38	52	38	42
76			0.986	0.991	52	35	45	38	41	47	34	48
77			0.987	0.986	61	36	46	27	41	56	34	39
78			0.992	0.987	54	36	51	29	40	51	40	39
79			0.985	0.996	50	33	52	35	38	47	37	48
80			0.988	0.984	52	31	49	38	33	52	40	45
81	90	10	0.988	0.983	54	40	50	36	39	55	42	44
82			0.988	0.982	55	40	53	32	43	52	42	43
83			0.989	0.971	54	36	55	35	42	49	43	46
84			0.986	0.983	56	37	52	35	43	51	40	46
85			0.987	0.985	57	35	53	35	43	50	41	46
86			0.950	0.990	58	40	47	35	44	54	36	46
87			0.988	0.982	57	38	51	34	42	54	39	45
88			0.987	0.990	57	39	51	33	44	53	40	43
89			0.987	0.988	56	35	54	35	41	51	42	46
90			0.990	0.987	53	41	49	37	40	55	39	46
91	95	5	0.987	0.996	57	40	55	38	43	55	42	50
92			0.987	0.991	59	40	53	38	46	54	41	49
93			0.987	0.993	59	41	53	37	46	55	41	48
94			0.995	0.987	62	38	55	35	47	54	42	47
95			0.987	0.994	61	39	52	38	46	55	40	49
96			0.992	0.988	58	42	56	34	45	56	44	45
97			0.987	0.991	59	41	54	36	44	57	42	47
98			0.987	0.987	57	41	55	37	42	57	43	48
99			0.987	0.997	56	40	56	38	43	55	43	50
100			0.994	0.987	58	39	57	36	44	54	44	48

. Subsequently, 60% of the sample is designated as the training set, while the remaining 40% is designated as the testing set for the experiment. Subsequently, the proportion of the testing set samples is increased gradually from 50% to 95%. Ten independent sets of experiments are conducted for each incremental increase in the training set samples until all 100 experiments are completed. The results of the experiment are presented in Table 6.

It is worth noting that in each experiment, the training and testing samples are randomly selected from the overall sample, which results in different item sizes and durations in each experiment. This means that the input variables are different combinations of values, as a way to ensure that different input variables do not affect the training results of the model. In order to elucidate the effect of variation in the training sample set on the accuracy of the training results, we also statistically analyzed the composition of the training set projects in each experiment. This includes the number of items of different sizes and the number of items of different durations. The specific data are shown in Table 6.

As evidenced by the data presented in Table 6, the R²-value of both the training set and the testing set in 100 experiments is approximately 1. This suggests that irrespective of the number of samples included in the training set and the testing set, the forecast values of the model exhibit a high degree of agreement with the actual observed values, thereby validating the model’s robust performance. Therefore, despite the relatively limited sample data employed in this study, the constructed RBF neural network demonstrates robust performance in project performance forecast, with the capacity to be applied to the forecast of project portfolios of varying sizes. The resulting forecast outcomes are found to be satisfactory.

4.3.4. Comparison and Analysis

In order to verify the superiority of the model in this paper, a linear regression analysis was performed on the data from 64 projects. We use linear regression and the RBF neural network constructed in this paper to forecast SPI(t₂) and SPI(t₃) for 64 samples, respectively, and the forecasting results are shown in Figure 7 and Figure 8. The data obtained from the linear regression analysis are compared with the data obtained from the model constructed in this paper, as shown in

Table 7. Comparison of the linear regression model and the RBF neural network model.

	The Linear Regression Model	The RBF Neural Network Model (95% as Training Set, 5% as Testing Set)
		1	2	3	4	5	6	7	8	9	10
R2 of SPI(t2)	0.989	0.987	0.987	0.987	0.995	0.987	0.992	0.987	0.987	0.987	0.994
R2 of SPI(t3)	0.637	0.996	0.991	0.993	0.987	0.994	0.988	0.991	0.987	0.997	0.987

. It can be seen that although the R² of SPI(t₂) obtained by linear regression is 0.989, which is extremely close to 1, the R² of SPI(t₃) is lower, which is only 0.637. This indicates that although the linear regression model has a better forecast effect on SPI(t₂), the forecast effect of SPI(t₃) is poorer.

On the contrary, the RBF neural network model constructed in this paper extends the sample size from 64 to 200 by expanding the data samples. Then, 95% of the samples are selected as the training set and 10 groups of independent random experiments are conducted. At this time, both the SPI(t₂) and SPI(t₃), whose R² values are closer to 1, can better forecast the project performance indicators and thus provide help for assessing project resilience.

4.3.5. Resilience Assessment

For the forecasted project performance results obtained, we assess the resilience of the project to the disruption E₁ by means of the project resilience assessment model. Using sample 1 as an example, its project resilience level is calculated through Equation (3). It can be seen that the SPI is 1 before project 1 encounters a disruptive event, and at the moment of t₂, the SPI drops to a minimum value of 0.7597, and finally, relying on the project’s own resilience and assessment, such as the reallocation of project resources, the SPI is restored to 1. According to Equation (3), the real resilience of project 1 is obtained as φ_real-1 = 1. The forecast of project performance through the constructed network model yields the SPI (t₂) forecasted result is 0.769 and the SPI (t₃) forecasted result is 0.988. Calculated according to Equation (3), the project resilience forecasted result φ_pre-1 = 0.948. By analogy, the true resilience value φ_real-2 = 1.604 and the forecasted resilience value φ_pre-2 = 1.456 can be calculated for Project 2. The relative error between the forecast and the true value is less than 10%, which indicates that the model is able to effectively forecast the resilience level of the past projects in the completed portfolio. This forecast indicates that project sample 1 has a high level of resilience and that the project schedule has a strong ability to cope with disruption and to take recovery assessments and return to the initial level after a disruption. The following Figure 9 shows the comparison between the forecast and true value of project resilience for the datasets.

A comparison of the forecasted and actual value of project resilience (Figure 9 and Figure 10) reveals that the majority of project resilience values fluctuate above and below 1, and the forecasted accuracy is high, with error values below 10%. By analyzing the project resilience, the project performance level can be determined, thereby assisting the project manager in evaluating the acceptability of the recovery schedule. If the project schedule is slower than the planned schedule, corrective actions are required to reduce the recovery time. Based on the RCF technique, the proposed model forecasts project disruption and recovery profiles based on previously observed trends in the portfolio. In our sample, the accuracy of the forecasts is improved by taking into account the actual performance knowledge of a reference class of comparable projects rather than relying on expert estimates. In other words, it allows managers of data-driven organizations to understand the behavior of similar projects in the face of disruption based on what has already happened in the portfolio.

4.4. Case Study

In order to demonstrate the practicality of the model developed in the paper, a specific case is selected as the background of the project for project resilience assessment. The name of the selected project is Claeys-Verhelst Premises, which is a commercial building. The expansion of the company premises of sanitary specialist Claeys-Verhelst, located in Oudenburg (Belgium), through the construction of a new three-floor building harboring a warehouse, office space, a small showroom, and recreational facilities for the employees. The start date of the project is 17 April 2016. The expected duration of the project is 442 days, and the expected cost is 3,027,133 €. The risk expectation for this type of project is 0.7, obtained through expert experience. BAC, PD, and LD of the project and the SPI value of the moment (SPI = earned value of completed work/planned work; assume that the work has already started at this moment and SPI = 1) are entered into the model constructed in this paper for forecasting. The information of the Claeys-Verhelst Premises project is shown in

Table 8. The information of Claeys-Verhelst Premises project.

Project Name	BAC	PD	SPI(t1)	LD	SPI(t2)	SPI(t3)	φ
Claeys-Verhelst Premises	3,027,133	442	1	0.7	0.3257	0.9616	0.943

.

Firstly, we input the relevant information of the project as input variables into the model constructed in this paper. The SPI(t₂) = 0.3257 and SPI(t₃) = 0.9616 of the project are obtained. Then, the project resilience is calculated as 0.943 according to Equation (3). The model constructed in this paper shows that the resilience of the project is less than 1, which indicates that the project’s ability to cope with challenges is weak. It may be difficult for the project to maintain the stability of its original plan or objectives in the face of external disturbances or changes, and it is prone to deviations or delays. It also reflects the project leader’s inadequacy in risk management, failing to adequately identify, assess, and respond to potential risks and challenges. In order to ensure that the project is not delayed, in this case, the project leader can make use of tools such as project management software (https://www.projectmanagement.ugent.be, accessed on 13 August 2024). to track the progress of the project in real time, including the completion of tasks and the use of resources, when work has already started. Measures can also be taken to develop a flexible and adjustable project plan, improve teamwork and communication skills, and establish a rapid response and decision-making mechanism. The implementation of these strategies will help the project maintain stability, flexibility, and quick recovery in the face of various uncertainties, challenges, and risks. This will ensure that the project reaches its desired goals.

5. Discussion

In the field of project management, objectivity is critical. Decision makers often rely on personal intuition and experience to make important decisions, leaving decisions unsupported by data and leading to potential project failure. This paper proposes an external approach that leverages data-driven methods to identify risks and opportunities, optimize resource allocation and utilization, and forecast changes in project performance after encountering disruption. The subsequent two subsections present these insights according to the different phases of the project lifecycle.

5.1. Preliminary Planning Stage

Effective strategic planning is critical in the initial stages of any project. Using a forecasting methodology allows the project manager to make a thorough assessment of the project requirements, potential risks, and challenges. This, in turn, enhances the understanding of the management approach, thereby ensuring project resilience and ultimately improving project outcomes. The assessment of project resilience, as demonstrated by projects 1, 4, and 5 in Figure 10, which have a project resilience of less than 1, allows the project manager to make informed decisions regarding investment. These include the option of not investing from the outset of the project or modifying the project schedule and budget. This enables the project manager to offset the potential for investment failure. In addition, the framework allows for the development of schedules that prioritize resilience by applying performance metrics to forecast performance in subsequent life cycle stages. If the project manager foresees that the performance level in the current schedule is lagging behind, other options should be evaluated and researched to change the schedule until an acceptable level of project performance is achieved. By analyzing Figure 9 and Figure 10, it can be seen that most of the project resilience levels are around 1, which means that the project performance can meet the schedule’s progress requirements. If the performance indicators are not met, the project funder can proactively implement financial incentives/disincentives and rationalize the allocation of resources so that the project performance can reach the expected level; or it can reject the project from the preliminary planning stage and select a more suitable project for investment.

5.2. Project Execution Stage

Resilience assessments provide important insights for project management during the project execution stage. By assessing resilience, project teams can establish effective monitoring systems, utilize timely and updated database indicators to identify problems, and make flexible adjustments. In this way, projects can quickly adapt to changing circumstances while maintaining their objectives. Resilience assessment plays a critical role in responding to disruptions and solving problems. Unforeseen disruption and issues may arise during project implementation. By anticipating changes in performance levels, the project team can proactively respond to unforeseen circumstances, implement timely and effective preventive measures, restore the project to its initial performance level, or decide whether to terminate the project in order to optimize project benefits. For example, for projects 14, 28, and 34 (Figure 9), the origin project resilience level is lower than 1, implying that project performance cannot be restored to the original level after the project encounters disruption during the implementation phase. At this point, the decision maker can use the quantitative information to rationalize the allocation of project-related resources or streamline work procedures to improve the final performance level and enable the project to achieve the expected results.

6. Conclusions

Construction projects are essential for the continued functioning of modern society, as they play a critical role in improving the country’s economic status. However, these projects face inherent complexity and interdependency that hinder their performance and cause various disruptions (such as delays to schedules and cost overruns). These disruptions can ultimately result in long-term consequences, including legal claims, disputes, and dissatisfaction among stakeholders. In order to mitigate the impact of project disruption, it is necessary to assess the level of project resilience. Nonetheless, while assessing project resilience is critical for supporting decision-making, prior research seldom employs theoretical models to tackle this problem. The absence of an objective assessment of project resilience and its influence on the project implementation process limits the development of high-quality construction projects. This model overcomes the limitations of subjective judgments and intuition. This paper presents an approach to project performance forecasting. It combines the RCF technique and RBF neural network to construct a model that uses completed historical project data as a database for training and validation. This approach enables the assessment of project resilience with greater accuracy.

The research in this paper is not without limitations. An important limitation lies in the construction of the RBF neural network, which is based on a limited dataset consisting of 64 construction projects. This information set, although representative, is not sufficiently comprehensive to cover the large number of project types that exist in the construction industry. Therefore, the generalizability of the findings may be limited to projects that are very similar to those in the dataset. Given the inherent complexity and variability of construction projects, there is a need for a broader and more comprehensive dataset to fully reflect project types and their unique characteristics. In addition, the assessment model constructed in this paper only focuses on indicators in terms of cost, duration, and risk level of the project, and the results of the study have some limitations.

Despite these limitations, this study opens several avenues for further research. Firstly, the mathematical model developed in this paper has wide applicability and has the potential to forecast the performance of various construction projects. Building on this foundation, future research can extend the functionality of the model by incorporating additional metrics such as stakeholder satisfaction and project effectiveness. These indicators would provide a more comprehensive view of project performance and could enhance the comprehensiveness of the forecasted results. In addition, incorporating long-term indicators into the model can provide more insight into project resilience and its evolution over time. This is particularly useful for assessing the sustainability and long-term success of construction projects. In addition, exploring the use of advanced machine learning techniques and algorithms could further refine the forecasted capabilities of the model, potentially leading to more accurate and reliable performance forecasts. In conclusion, there are substantial opportunities for future research to expand and extend the results of this study, contributing to a more nuanced and comprehensive understanding of the resilience of construction projects.