DA in ETO processes: managing engineering changes in configuration

DA is largely discussed in the literature. In this paper, we adopt the definition of DA by Cederfeldt and Elgh (Reference Cederfeldt and Elgh2005): ‘computerised automation of tasks that are related to the design process through the implementation of information and knowledge in tools or systems’. There is a significant amount of literature on the technical aspects of DA, but there is relatively little literature on its applications in the ETO industry. Researchers have proposed recommendations for planning design automation in ETO companies, including an information model for design automation in quotation preparation (Elgh, Reference Elgh2012) and the need for a design automation framework based on a study with ETO manufacturers (Cederfeldt and Elgh, Reference Cederfeldt and Elgh2005).

According to Haug et al. (Reference Haug, Ladeby and Edwards2009), transitioning from ETO to mass customization involves considering five critical dimensions for determining the appropriate level of standardization and automation: product variety, customer perception, manufacturing costs, business objectives, and configurator challenges. These dimensions vary based on the challenges and disparities between mass producers and ETO companies during the transition to mass customization (Davis, Reference Davis1987). In the context of mass producers, fostering product variety is essential, whereas ETO companies need to adopt limitations in this aspect. From a customer’s perspective, customization must offer tangible value; otherwise, it may lead to disorientation. Although customization typically incurs higher manufacturing costs, effective management can keep prices comparable to mass-produced products. The primary purpose of adopting mass customization is to boost sales. Customers in mass-production companies have more limited design choices than ETO companies, where configurator design is crucial. Conversely, ETO companies face the main challenge of finding the right balance between design flexibility and standardization. In turn, Haug et al. (Reference Haug, Ladeby and Edwards2009) suggest that during the transition to mass customization, careful consideration of these five dimensions is pivotal to successful implementation and adaptation to the specific needs of both mass producers and ETO companies.

DA for highly customized ETO products typically involves developing and implementing IT applications such as sales (Hvam et al., Reference Hvam, Pape and Nielsen2006) and engineering configurators (Mäkipää et al., Reference Mäkipää, Paunu and Ingalsuo2012), as well as linking them with CAD systems (Raffaeli et al., Reference Raffaeli, Mengoni and Germani2013). While product lifecycle management (PLM) systems are often seen as enabling the sharing of product data across supply chains or product lifecycles (Silventoinen et al., Reference Silventoinen, Pels, Kärkkäinen and Lampela2011), their effectiveness in ETO environments is still uncertain (Hicks and McGovern, Reference Hicks and McGovern2009). Standard and configurable components, common in make-to-order (MTO) products (Lee and Lee, Reference Lee and Lee2014), can be stored and retrieved for reuse with various IT applications. However, these approaches do not adequately address the unique requirements of ETO environments, such as the need for creative design tasks for order-specific solutions (Zhang, Reference Zhang2014). There have been some efforts to address the challenges of design automation in ETO environments, including proposals for a product structure concept that promotes the reuse of order-specific solutions (Brière-Côté et al., Reference Brière-Côté, Rivest and Desrochers2010) and the development of a system-level configurator that handles incomplete configurations and engineering changes (Kristianto et al., Reference Kristianto, Helo and Jiao2015). Design automation in ETO processes has several limitations that can impact the efficiency and effectiveness of the engineering process. Some of the main limitations emerging from the literature are:

• • Complexity: ETO processes often involve complex products that require a high level of customization, which makes it challenging to automate the design process (Thomassen and Alfnes, Reference Thomassen and Alfnes2017). The complexity of the product may require specific engineering expertise. Indeed, the externalization of tacit knowledge (Yi, Reference Yi2006) cannot be easily automated, making it difficult to apply DA;

• • Lack of standardization: due to the high level of customization needed, ETO processes typically lack standardization, which makes it difficult to automate the design process. The lack of standardization may require manual intervention, resulting in increased engineering time and costs (Haug et al., Reference Haug, Ladeby and Edwards2009);

• • Interdisciplinary collaboration: DA often requires collaboration across different disciplines. Collaboration across these disciplines can be difficult to automate and requires careful coordination to ensure that all aspects of the design are integrated correctly (Heikkinen et al., Reference Heikkinen, Johansson and Elgh2020). In general, it may be necessary to implement dedicated methodologies to make explicit the DA processes (Curran et al., Reference Curran, Verhagen, Van Tooren and Van Der Laan2010), particularly when an ETO production approach is adopted by a company (Bakker et al., Reference Bakker, Boehme and van Donk2012);

• • Customer requirements: ETO processes are driven by customer requirements, which can vary significantly, and meeting these requirements often requires manual intervention to ensure that the design meets the customer’s needs (Cederfeldt, Reference Cederfeldt2007).

Overall, design automation can be challenging in ETO processes due to the high level of customization needed and the need for interdisciplinary collaboration and accurate data management. Furthermore, the current state of DA in ETO is limited, and further research is required in order to address these environments’ unique challenges and requirements.

Methods and tools that can enable DA in ETO processes

The limitations presented in Section “DA in ETO processes: managing engineering changes in configuration” can be addressed through methods that find optimal designs by means of techniques that do not rely on predetermined solutions (Amadori et al., Reference Amadori, Tarkian, Ölvander and Krus2012) and could support DA processes in dealing with ETO constraints and multi-objective function design problems.

Among the strategies that address these needs, some methods use randomized fluctuations in the design variables, such as genetic algorithms (GAs) (Forrest, Reference Forrest1996), while others avoid the direct adjustment of design variables entirely by employing learning algorithms (Sobieszczanski-Sobieski et al., Reference Sobieszczanski-Sobieski, Morris and Van Tooren2015).

Machine learning (ML) techniques are used to teach machines how to handle data more efficiently (Mahesh, Reference Mahesh2020). In this context, the work of Eichhoff and Roller (Reference Eichhoff and Roller2015) includes a review of ML approaches to support configuration and parameterization in design exploration and optimization through the elaboration of information and relationships. ML relies on different algorithms to solve problems of diverse nature, such as supervised learning (Cunningham et al., Reference Cunningham, Cord and Delany2008), unsupervised learning (Barlow, Reference Barlow1989), semi-supervised learning (Reddy et al., Reference Reddy, Viswanath and Reddy2018), instance-based learning (Kramer, Reference Kramer2013) and ANNs, which are a type of ML algorithm inspired by the structure and function of the human brain. They consist of layers of interconnected “neurons” that can process and transmit information. ANNs can be trained to recognize patterns and make decisions based on input data. They are commonly used for tasks such as image and speech recognition, natural language processing, and predictive modeling (Bishop, Reference Bishop1994). ANNs implement algorithms that aim to achieve neurological-related performance through a group of multiple perceptrons or neurons at each layer. Their history began in the early 1940s, and they historically have been used for engineering control systems (Meireles et al., Reference Meireles, Almeida and Simões2003) and other engineering industrial problems where physical processes are not well understood or are highly complex, with uncertainties that justify their utilization (Fukuda and Shibata, Reference Fukuda and Shibata1992).

One of the possible benefits of using ANNs in DA processes for ETO purposes could be their ability to process large amounts of data quickly (Woldemariam and Lemu, Reference Woldemariam and Lemu2019). This can be particularly useful when it is difficult to identify a suitable a priori design optimization model. However, one limitation of ANNs is that they may not perform well when faced with inputs significantly different from those used in the training phase. This can be especially problematic when trying to extrapolate results beyond the training inputs’ range, as Bishop (Reference Bishop1994) pointed out. In these cases, the network may not respond accurately to the new inputs, leading to unreliable results.

Table 1 summarizes the approaches used to address the challenges of DA processes in the ETO industry.

Table 1. Approaches that can support DA processes in the ETO industry

In this research, we propose an integrated method that utilizes ANNs to reduce the need for massive simulations in the design process and to suggest an optimized design configuration in the ETO sector, specifically for complex turbomachinery systems. Unlike new product development (NPD) environments, where active exploration of entirely new design spaces is common (Takeuchi and Nonaka, Reference Takeuchi and Nonaka1986), ETO involves the customization of existing products to meet specific client requirements. In this context, there is often a wealth of historical data from prior designs and simulations, allowing us to build a robust ANN model using pre-existing CFD simulations. This approach reduces engineering cycle times and enables rapid optimization of multiple conflicting design parameters (Zhou and Ooka, Reference Zhou and Ooka2021). The novelty of our work lies in the integration of ANNs – as an enabler – within DA processes specifically tailored for the ETO sector, where the focus is on adapting and optimizing designs quickly, as opposed to creating entirely new configurations from scratch.

We acknowledge that active learning approaches, such as Bayesian optimization (Shahriari et al., Reference Shahriari, Swersky, Wang, Adams and De Freitas2015) and Gaussian process models (Tyagi et al., Reference Tyagi, Yang, Tyagi and Dwivedi2011), could further reduce the reliance on large datasets by selectively generating new data points as needed, particularly when working in new or unexplored design spaces like in the case of NPDs (Bae et al., Reference Bae, Nam and Kang2024). However, our current approach is tailored to environments where a significant amount of simulation data is already available, as the case in ETO applied to turbomachinery industry typically is.

In the following subsection, a deeper literature review on ANNs has been carried out, focusing on applications in the turbomachinery industry that have been used as a starting point for this work and whose limitations we tried to overcome, as we assumed of using ANNs for enabling DA processes in the ETO industry.

A focus on ANNs: a metamodel for the turbomachinery industry

In order to reduce the number of expensive simulation calls during the optimization of problems like the one presented in this paper, surrogate models are generally employed (Wu et al., Reference Wu, Sotnikov, Gary Wang, Coatanea, Lyly and Salmi2023). Historically, simulation metamodeling is commonly performed through ANNs (Fonseca et al., Reference Fonseca, Navaresse and Moynihan2003). Many different types of neural network models have been developed over the years, but among the most common in industrial applications are the multilayer perceptron (Gardner and Dorling, Reference Gardner and Dorling1998) and the radial basis function network (Orr, Reference Orr1996). These two methods are the foundation of many practical applications (see the review of Meireles et al., Reference Meireles, Almeida and Simões2003) and are of particular interest in this work. They belong to a general class of neural networks known as feed-forward networks (Bebis and Georgiopoulos, Reference Bebis and Georgiopoulos1994), which have been the subject of extensive research in recent decades (Abdolrasol et al., Reference Abdolrasol, Hussain, Ustun, Sarker, Hannan, Mohamed and Milad2021). Feed-forward networks are the most popular type of neural network algorithm in engineering applications (Wu and Wang, Reference Wu and Wang2021), thanks to their ability in learning patterns and relationships directly from data, making them suitable for optimization tasks where the underlying physics is complex or not fully understood (Edlan and Shamir, Reference Eldan and Shamir2016). By training on relevant data, feed-forward networks can uncover intricate interactions between design parameters and performance metrics, leading to improved optimization results (Xu et al., Reference Xu, Liu, Cao, Huang, Liu, Qian and Zhang2021). A feed-forward neural network can be considered a non-linear function that transforms input variables into a set of output variables through a series of hidden layers (cfr. Figure 1). Each hidden layer (see the layer where D and E are in Figure 1) is a layer between the input (A, B, C) and output (F) layers that performs the transformation between weighted inputs and outputs using a set of parameters (weights) determined through a learning or training process (Wu and Wang, Reference Wu and Wang2021).

Figure 1. Structure of a feed-forward neural network, as schematized by Wu and Wang (Reference Wu and Wang2021).

This process can be computationally intensive, but once the weights have been determined, the network is able to process new data quickly. The training phase of a neural network involves adjusting the weights to produce the desired responses. The goal of any learning algorithm is to find the values of the weights that minimize an appropriate error function (Bishop, Reference Bishop1994).

ANNs have been widely used in the turbomachinery industry for simulations and predictions of the performance of various components, such as gas turbines (Lazzaretto and Toffolo, Reference Lazzaretto and Toffolo2001), axial compressors (Yu et al., Reference Yu, Chen, Sun and Wu2007), and centrifugal compressors (Ghorbanian and Gholamrezaei, Reference Ghorbanian and Gholamrezaei2009; Jiang et al., Reference Jiang, Dong, Liu, He and Ai2019). Nevertheless, these applications often tend to concentrate solely on the performance of individual components, disregarding the potential impact that variations in internal design parameters may have on overall performance. Ghorbanian and Gholamrezaei (Reference Ghorbanian and Gholamrezaei2007) conducted a comparison between several types of ANNs for simulating the performance of axial compressors and demonstrated that some of them deliver results aligned with experimental data. In recent years, ANNs have also been utilized for optimizing the layout of turbomachinery components (Du et al., Reference Du, Li, Yang, Liu, Zhang and Xie2022) and for design optimization as a surrogate model to reduce computational efforts, with respect to more robust optimization methods (i.e., GA), when a large amount of data is available (Woldemariam and Lemu, Reference Woldemariam and Lemu2019). Applications have been conducted on centrifugal impellers (Ji et al., Reference Ji, Wang, Tang and Xi2021), radial turbines (Luczynski et al., Reference Luczynski, Hohenberg, Freytag, Martinez-Botas and Wirsum2021), and fan blades (Lopez et al., Reference Lopez, Ghisu and Shahpar2022). Similar to the abovementioned papers, these applications mainly focus on the shape optimization of single components and do not involve complex systems studies.

Derakhshan et al. (Reference Derakhshan, Mohammadi and Nourbakhsh2010) proposed a comparison between GAs and ANNs to optimize the shape of the radial blade. In both these cases, the analysis focuses on a single component.

ANNs represent an alternative computational approach in which the solution to a problem is derived from a set of samples rather than relying on explicit instructions as in traditional calculation methods. In this context, one of the main advantages of using ANNs in advanced DA models is the ability to quickly process large amounts of data (Rojas, Reference Rojas2013). Furthermore, ANNs can learn and then approximate relationships between inputs and outputs independently from the complexity and size of the problem (Haykin, Reference Haykin2004). However, a disadvantage of ANNs is that they may not perform well when faced with inputs significantly different from those used during the training phase or when attempting to extrapolate results to regions where the inputs are substantially different from those used in the training phase (Bishop, Reference Bishop1994).

A summary of ANN-based approaches that have been reviewed is shown in Table 2, according to the objective of the related study to highlight their advantages and limitations from the perspective of their potential in DA processes.

Table 2. ANN-based approaches in the ETO turbomachinery industry and the related potential for supporting DA

In this section, a literature review has been carried out to highlight the DA models adopted in design processes in ETO-structured companies. The ANN-based tools and methods used in the turbomachinery industry that can enable DA processes in the ETO industry have been outlined to answer RQ1.

Limitations and research gaps have been highlighted to ensure the robustness of the design process of BH RC cylinders. The methodology proposed in the following sections aims to guarantee both the repetitiveness of the task and the possibility of customizing the product by meeting the lead time needed by the customer. Overall, from the literature review, it emerges that the integrated approach combining ANNs and DA methods for RC cylinder design has the potential to generate significant benefits in industrial practice, including improved design efficiency, enhanced performance, cost reduction, knowledge generation, and a competitive advantage in the turbomachinery industry. In the following sections, the methodological approach and the integrated DA method that constitute the main original contribution of this work will be presented and validated through real job applications to answer RQ2.

Overview of the proposed process

The proposed method converts input variables given by the customer, such as flow rate and gas composition, into an optimized and validated cylinder configuration, thanks to the integration within the same process of DA methods and tools specifically embedded for this purpose.

The proposed method is schematized in Figure 3 using the IDEF0 model (Presley and Liles, Reference Presley and Liles1995). The arrows on the left summarize the inputs, the ones from the top represent the rules, the constraints, and the models, and the ones from the bottom represent the resources, while the arrow on the right of the block represents the output of the method.

Figure 3. Level 0-IDEF0 representation of the new RC cylinder design development process.

In Figure 3, the black lines represent the flows that already exist in the design process of RC cylinders described in Section “Research methodology” (cf. Figure 2). Blue lines mark the new models and rules of the proposed DA process, red lines refer to integrated functions of the tools and resources suggested in this study, and green lines represent the innovative output of the process with respect to the as-is process.

The integrated design development process is herein further detailed (see also the Level 1-IDEF0 diagram in Figure 4):

• - Box A3 of Figure 4: preliminary RC cylinder parameters from the BH thermodynamic and mechanical calculation tool, which delivers the overall layout of the compressor, are used in a product configurator that embeds several knowledge-based 3D master models (i.e., one for each family of cylinders) to sketch the preliminary solution to be optimized according to customer requirements. The choice of the rule-based software Siemens Rulestream (https://plm.sw.siemens.com/en-US/teamcenter/solutions/product-configuration-management/, last access on 03/11/2023) has been made to ensure interoperability with the set of tools already used by the BH engineering department, such as the 3D CAD software Siemens NX (https://plm.sw.siemens.com/it-IT/nx/manufacturing/, last access on 03/11/2023) and the PLM Siemens Teamcenter (https://plm.sw.siemens.com/en-US/teamcenter/, last access on 03/11/2023). This software also allows the implementation of rules and constraints deriving from BH regulations and standards within the master model.

• - Box A4: preliminary parameters are orchestrated by the software Simulia Isight (https://www.3ds.com/it/prodotti-e-servizi/simulia/prodotti/isight-e-simulia-execution-engine/, last access on 03/11/2023) to obtain the optimal RC design configuration that targets the goal parameters. This software has been chosen to orchestrate the ANNs MATLAB routine to deliver the optimal parameters of the DA master model thanks to its ability in managing the flow of information. Usually, Isight is used at BH to conduct sensitivity analyses, parametric studies, and design optimization. It can easily automate the execution of ANNs for the purpose of this research, ensuring robustness in the choice of the optimal set of parameters that meet the target parameters.

• - Box A5: optimized parameters are implemented in Rulestream to obtain the required final configuration of the cylinder, which can then be included in the final overall thermodynamic and mechanical calculation of the whole compressor to be declared to the customer.

Figure 4. Level 1-IDEF0 Representation of the new RC cylinder design development process.

Figure 5 shows how the different tools are combined together. As outlined before, the process begins with a preliminary configuration tool that defines the initial design parameters. This tool ensures that the base design characteristics are set and ready for further refinement. After the initial configuration, Rulestream is used to create a preliminary 3D model based on the initial design parameters. This stage helps visualize the design early in the process and check for basic compliance with design rules. The Isight tool is used to orchestrate the ANNs during the optimization process. Here, the preliminary set of parameters is refined, resulting in an optimal set of parameters. Isight automates the optimization, adjusting the design based on the target parameters in terms of flow coefficient and clearance volumes. With the optimal set of parameters identified, Rulestream is used once again to generate the final, optimized 3D configuration. This ensures that the design follows all the optimization steps and is ready for final validation.

Figure 5. Flowchart showing how the different tools are combined.

The following subsections provide further details about the process and the diverse components of the proposed DA workflow.

Critical parameters for RC cylinder design

One of the most critical parts in the design of RCs and one of the main problems in their design is related to the pressure losses that are generated as the gas flows through the passages of the gas ducts, particularly in the section of the valve pocket, including valves and gas ducts between them and the compression chamber within the cylinders. Optimizing the shape of the gas ducts of a RC’s cylinder can provide several benefits for a company in the market, such as:

• • Improved efficiency: optimizing the shape of the gas ducts can help reduce energy losses due to turbulence, improving the compressor’s overall efficiency.

• • Enhanced performance: by optimizing the gas ducts, the compressor can achieve higher flow rates and pressures, which can be beneficial in applications where high levels of compressed gas are required.

• • Increased reliability: optimizing the shape of the gas ducts can help reduce the likelihood of mechanical failure due to stress, fatigue, or other factors.

Differentiation: by optimizing the shape of the gas ducts, a company can differentiate its products from those of its competitors. In summary, optimizing the shape of the gas ducts of a RC’s cylinders brings several advantages mainly related to efficiency and performance. Indeed, the waste of energy is relevant in a geometry as complex as that of a valve pocket. Therefore, its evaluation becomes a critical aspect for the analysis of the cylinder performance mainly for two reasons:

• • The pressure drop observed in the valve pocket is an index of the valve’s effectiveness, which is crucial for the work needed to compress the gas.

• • The relationship between the pressure drop and the mass flow rate must be known during the entire cylinder design process since it is the base of the mathematical model for calculating the p-V cycle characteristic of the compressor.

Additionally, clearance volumes, also known as dead volumes, significantly impact the volumetric efficiency and overall performance of a machine. As the piston reaches the top dead center during the discharge phase, a portion of the gas volume remains uncompressed. The negative impact of clearance volumes on the suction capacity increases with both the size of the clearance volume and the compression ratio.

DA master model

This research focuses on the analysis of a vast database developed by BH, which examines the BH’s complete fleet of RC cylinder families, consisting of over 365 unique cylinders. For each RC cylinder family included in the database, we built a master model of the cylinder assembly suitable to communicate with the other steps of the process. This model considers the critical parameters outlined in Section “Critical parameters for RC cylinder design” and is built to embed the quantitative and qualitative parameters describing the gas flow path that are detailed in Section “Dataset development from the BH archive”. The 3D model is developed through the CAD software Siemens NX. It is a knowledge-based and fully parametric model of an RC cylinder assembly of components embedding all the parameters necessary for the design optimization to goal the target parameters of the study. As this study focuses on the gas pressure losses along the cylinder valve pocket flow path, a finite number of parameters that define the layout of the cylinder geometry in this area, the valve properties, and the cylinder head topology are considered in the master model. These parameters are implemented in a Rulestream model (an example of a master model of a cylinder family made of nodular cast iron is shown in Figure 6), which includes the rules related to the design of an API 618 BH RC cylinder to communicate on different sides of the design process chain with the CAD, PLM software and the optimization tool. This can manage consistent changes in configuration by monitoring and maintaining the constraints of a robust design to overcome the limitations related to the exploration of solutions that are not part of automatically generated design configurations.

Figure 6. Rulestream model for a nodular cast iron 12 valves-cylinder family.

Dataset development from the BH archive

The common practice at BH is to determine the total losses of a machine through CFD analyses. The total losses are summarized in the global flow coefficient $ {K}_{\mathrm{s}} $ and the clearance volume value $ \varepsilon $ . The flow coefficient $ {K}_{\mathrm{s}}=\frac{{\dot{m}}_{\mathrm{real}}}{{\dot{m}}_{\mathrm{id}}} $ represents the ratio between the actual and ideal gas flow rates through the RC valves, which is necessary to obtain the real mass flow rate through the same valve once the pressure drop has been established. The clearance volume $ \varepsilon =\frac{{\mathrm{V}}_{\mathrm{TDC}}}{V_{\mathrm{C}}} $ represents the percentage of the volume remaining among the piston, cylinder head, and valves of an RC cylinder when the piston reaches the top dead centre relative to the cylinder capacity. DEs can monitor these two parameters to assess the performance of the RC cylinder and calculate the absorbed power declared to the customer, which is a function of both $ {K}_{\mathrm{s}} $ and $ \varepsilon $ :

$$ {\mathrm{P}}_{\mathrm{ABS}}=f\left({K}_{\mathrm{s}},\varepsilon \right) $$

To obtain these values, extensive simulations are needed, with a single cylinder taking approximately 10 hours of computation on a six core-processor able to parallelize the run. In the past, most studies focused solely on analyzing valve pressure losses. However, with changes to gas duct layouts over time, the losses of all the other components of the machine have become crucial. CFD simulations have shown potential for studying the entire reciprocating compressor but are limited by high computational costs. Unfortunately, such analyses’ timing often conflicts with BH ETO process schedules, making it challenging to allocate sufficient resources and computational time. Therefore, there is a need to explore innovative methods to quickly design RC cylinders that can meet customer demands.

The database used for this work and available through tools owned by BH includes for every cylinder:

• • Cylinder name, with a code that identifies the cylinder;

• • Cylinder bore;

• • Cylinder valves size and number;

• • Six geometric parameters describing the gas flow path layout. Indeed, several factors influence the performance of the cylinder concerning $ {K}_{\mathrm{s}} $ and $ \varepsilon $ . These include distances, angles, and cylinders component dimensions;

• • $ {K}_{\mathrm{s}} $ for the two phases (i.e., suction and discharge), both at the head and crank-end of the cylinder;

• • $ \varepsilon $ both for the head and crank-end of the cylinder and the medium value between the two.

To simplify the analysis, the database was rearranged as follows: $ {K}_{\mathrm{s}} $ was evaluated for the suction phase of the head-end side of the cylinder, and the medium value between the head and crank-end side of the cylinder was considered for $ \varepsilon $ . This approach analyses only the suction phase of the head-end side of the cylinder, resulting in eight independent parameters and two dependent variables ( $ {K}_{\mathrm{s}} $ and $ \varepsilon $ ) for each of the 365 different cylinders in the original database. While some variables, such as the number and size of valves, are discrete with standard values, other variables are represented as discrete geometrical values that could theoretically be continuously altered by an ANN. Based on the analysis of this heterogeneous database, the physics of the problem, and the literature reviewed in Section “Related work and state-of-the-art”, a metamodel is developed to represent the independent variables affecting the two dependent variables. This metamodel is presented in the following subsections.

To understand how the different variables are distributed in the design space of the dataset and how they are correlated to each other, a correlation matrix plot is presented in Figure 7. Variables have been clustered according to their nature within the dataset. Geometrical and quantitative parameters describing the gas duct are highlighted in blue, while the relationship between the two variables representing the performance of the cylinder and their distributions are highlighted in green. The correlations between each parameter of the first type and each of the parameters of the second type are highlighted in orange. In this chart, each off-diagonal subplot contains a scatterplot of pairs of variables with least-squares reference lines with slopes equal to the displayed correlation coefficients, while each diagonal subplot contains the distribution of the variable as a histogram. Additionally, each cell of the correlation matrix shows the correlation coefficient, which measures the strength and direction of the linear relationship between two variables. It quantifies how closely the variables are related to each other. The correlation coefficient typically ranges from −1 to +1. Values close to +1 or − 1 suggest a strong correlation, while values closer to 0 indicate a weaker correlation.

Figure 7. Correlation matrix between all pairs of variables.

For confidentiality reasons, the geometrical parameters of the various cylinders present in the database are herein masked and shown as Var1 to Var8. In Figure 6, the last two variables are related to the values of clearance volumes $ \varepsilon $ and flow coefficient $ {K}_s $ , respectively. The correlation matrix plot shows that, apart from the discrete variables (i.e., Var1, Var6, and Var8), most of the variables are sparsely distributed throughout the design space. It also demonstrates that some of them are moderately correlated (i.e., Var2 and Var3), others are strongly linearly correlated (i.e., Var6 and Var8), while other variables appear weakly correlated with each other (i.e., Var1 and $ \varepsilon $ ).

The dataset analysis reinforces the assumption to apply ANNs for the purpose of this research, as they can be particularly effective for handling heterogeneous and sparse data and for capturing complex, non-linear relationships when finding correlations between the different variables is difficult.

ANNs: training and performance estimation

The possibility that the application of ANNs can provide an optimal design solution for an RC cylinder outside the boundaries of the design space represented by its training dataset in place of more computationally expensive optimization methods is herein analyzed. With this purpose, the database has been prepared and imported into MATLAB, which has been chosen together with the BH IT department as the most suitable software for this analysis due to its extensive toolset, ease of use, and integration capabilities with the other BH tools with already available licenses. Within this development environment, a feed-forward algorithm has been implemented.

Ensemble modeling is a powerful technique that can help improve the performance and generalization of a machine learning model (Ganaie et al., Reference Ganaie, Hu, Malik, Tanveer and Suganthan2022). By training multiple neural networks and averaging their results, we can reduce overfitting, improve accuracy, and obtain more reliable uncertainty estimates (Yu et al., Reference Yu, Wang and Lai2008). This technique is beneficial when dealing with large and complex datasets, where a single neural network may struggle to learn all the underlying patterns in the data. Ensembling multiple networks can help capture a more diverse set of representations of the data and produce a more robust and generalized model (Kotu and Deshpande, Reference Kotu and Deshpande2014).

With this purpose, 30 feed-forward ANNs with a single hidden layer of size 20 were created and trained to correlate 8 input parameters describing the type and geometry of the cylinder to the 2 performance parameters (i.e., $ \varepsilon $ and $ {K}_{\mathrm{s}} $ ) as an output. The number related to the hidden layer size and number of ANNs for the ensemble modeling are the results of a trade-off obtained through a sensitivity analysis: the time needed for training and executing one calculation together with the output quality have been evaluated for various configurations of ANNs with different hidden layer sizes, ranging from 10 to 40 being equal to the number of ANNs (10), and for ensemble modeling, with a number of ANNs varying from 10 to 100 being equal to the hidden layer size (10). The quality of the output of ANNs (cfr. Tables 3 and 4) was assessed through the mean absolute percentage error (MAPE), defined as:

$$ \mathrm{MAPE}=\left(\frac{1}{n}\sum_{i=1}^n\left|\frac{x_{\mathrm{DB}}-{x}_{\mathrm{ANN}}}{x_{\mathrm{DB}}}\right|\right) $$

where $ {x}_{\mathrm{DB}} $ is the generic variable present in the database, $ {x}_{\mathrm{ANN}} $ is the same variable calculated by the ANN, and $ n $ is the number of samples present in the database.

Table 3. MAPEs obtained through different hidden layer sizes

Table 4. MAPEs obtained through different numbers of ensembled ANNs

The analysis concerning the training time related to the size of the hidden layer is reported in Figure 8, while the analysis regarding the number of ANNs is summarized in Figure 9.

Figure 8. The size of the hidden layer ranged from 10 to 40.

Figure 9. The number of ANNs of the ensembled model ranged from 10 to 100.

The ANNs used in this study were trained using MATLAB’s trainnet function, which automatically splits the dataset into training, validation, and test sets to ensure robust performance evaluation through a k-fold cross-validation approach. The training set is utilized to optimize the network’s weights, the validation set monitors the model to prevent overfitting, and the test set is used for final performance assessment on unseen data. This method ensures that the ANN is trained and evaluated on multiple data partitions, providing a comprehensive assessment of its performance across different data splits. Additionally, an ensemble of ANN models was created, where the final prediction was obtained by averaging the outputs of multiple models. This ensemble approach has been checked by the authors by comparing the variability of errors against the number of ANNs as shown in Table 4, confirming the model’s robustness.

To ensure that the performance of the RC machine meets the customer’s expectations, it is crucial to evaluate the impact of errors in the $ {K}_{\mathrm{s}} $ and $ \varepsilon $ values on the absorbed power. The ANNs’ quality has been verified by comparing the outputs generated by the ANNs to the same dataset sample. The accuracy of the prediction method was assessed using the MAPE for both the $ {K}_{\mathrm{s}} $ and $ \varepsilon $ variables.

$$ {\mathrm{MAPE}}_{K_{\mathrm{s}}}=\left(\frac{1}{n}\sum_{i=1}^n\left|\frac{{K_s}_{\mathrm{DB}}-{K_s}_{\mathrm{ANN}}}{{K_s}_{\mathrm{DB}}}\right|\right)=0.1\% $$

$$ {\mathrm{MAPE}}_{\varepsilon }=\left(\frac{1}{n}\sum_{i=1}^n\left|\frac{\varepsilon_{\mathrm{DB}}-{\varepsilon}_{\mathrm{ANN}}}{\varepsilon_{\mathrm{DB}}}\right|\right)=1.43\% $$

where:

• • $ {K_s}_{\mathrm{DB}} $ is the value of the flow coefficient present in the database;

• • $ {K_s}_{\mathrm{ANN}} $ is the value of the flow coefficient calculated with the ANNs;

• • $ {\varepsilon}_{\mathrm{DB}} $ is the value of the mean clearance volume present in the database;

• • $ {\varepsilon}_{\mathrm{ANN}} $ is the value of the mean clearance volume calculated with the ANNs;

• • $ n $ is the number of cylinders present in the database.

A MAPE on $ {K}_{\mathrm{s}} $ of 0.1% and on $ \varepsilon $ of 1.43% leads to an error of 0.1% on the declared absorbed power, which has been considered acceptable with respect to API 618 standard, as customers typically accept a larger tolerance on that value (3%). The difference between the two MAPEs can be addressed through the simplifications of the dataset, with respect to the averaged value of each clearance volume $ \varepsilon $ , summarised in Section “Dataset development from the BH archive”, while each value of the flow coefficient $ {K}_{\mathrm{s}} $ present in the database has been considered as-is.

A cross-check of the quality of the network has been made through the error histogram with respect to the clearance volume values (as it seems to be the parameter with the highest MAPE), which shows the distribution of errors between predicted and target values after training a feed-forward neural network. The histogram (cf. Figure 10) indicates that over 85% of the predictions had errors within a range of −0.23 to 0.15, with a relative error of 1.32% on the average clearance volume. These results demonstrate the reliability of the ANN for predicting the desired outputs in the environment.

Figure 10. Error histogram for clearance volume calculation.

ANN integration in the DA process

This subsection depicts the methodology aiming to integrate the ANNs in the overall design process by orchestrating the different parameters playing a crucial role in targeting customer requirements. This is described through an IDEF0 diagram (cf. Figure 11) with respect to process A4, as shown in Figure 4. The preliminary parameters of the baseline configuration are exported from Rulestream, which is used as a knowledge-based 3D configurator. The trained and validated ANNs are integrated and orchestrated into a DA tool able to deliver the optimal solution once the computational goals have been set. As outlined before, Isight is an orchestrator used to combine multiple models and multi-disciplinary applications into a simulation process flow, automate execution across distributed computing resources, explore the resulting design space, and identify optimal design parameters responding to the required constraints. The MATLAB routine of the feed-forward ANNs algorithm is managed by the orchestrator to goal the target values set as a computational input. The output of this run is the set of parameters of the optimized RC cylinder assembly, which are exported back into the configurator, that embeds the parametric 3D models to deliver the optimal configuration required by the customer. By exploiting the functionality of this integration, this method is able to communicate on both sides of the design process, from the preliminary layout to the optimal design configuration of the cylinder able to meet customer requirements.

Figure 11. ANNs orchestrated in the DA process.

Cylinders description

1. a. The first case (cf. Figure 12) is a non-routine design modification of the geometrical parameters present in the DA master model (i.e., the ones that describe the gas flow path between the valves and the compression chamber) of a cylinder, which is part of the dataset on which the ANNs have been trained. This cylinder is a standard forged steel cylinder with a total of 4 valves. The customer required a target value of absorbed power (which means $ {K}_s $ and $ \varepsilon $ ). It is necessary to modify the geometrical parameters of the gas path to meet customer requirements. This is a typical ETO job that is often performed by BH.

1. b. The second case (cf. Figure 13) is part of a new product development program planned after the customer’s request to increase the whole machine’s power density. The new cylinder is a member of a new family that is scaled up from an existing cast steel cylinder, with a total of 8 valves, which the ANNs have been trained on. Physically, this case study involves the development of a new cylinder with an overall shape similar to others already present in BH’s portfolio but with a different combination of parameters (i.e., geometrical parameters, such as the compression chamber bore, and architectural parameters, such as the total number of valves), placing this cylinder outside the design space proper of the dataset on which the related ANNs have been trained. The analysis aims to reach a goal value of performance similar to that of the existing family, which results in target values of $ {K}_s $ and $ \varepsilon $ . Targeting this performance, together with increasing the capacity of the cylinder, allows BH to meet the job’s requirements.

1. c. The third case study (cf. Figure 14) is part of the same project as the second one. Unlike the case study b, the baseline is an entirely new cylinder, especially in terms of the gas flow path. Unlike the other cylinders of the same family obtained by forged steel, this unique cylinder has a total of eight valves, which leads to a particularly innovative shape of the gas ducts. The overall layout of this cylinder places it outside the design space of the cylinder’s families on which the ANNs have been trained. In this case, the study aims to set a target value in terms of $ {K}_{\mathrm{s}} $ and $ \varepsilon $ , proper to cylinders with the same number of valves that are obtained by cast steel, which is the benchmark in terms of product competitiveness.

Figure 12. Cylinder of the first case study (a).

Figure 13. Cylinder of the second case study (b).

Figure 14. Cylinder of the third case study (c).

Pipeline execution

For each case study, the execution of the computational pipeline of the proposed integrated DA method has been carried out and its results have been compared with a complete CFD analysis performed separately with the cylinder configuration previously obtained through the DA method itself. This comparison is needed to verify the KPIs of the study.

CFD

With the obtained design configuration, a complete CFD analysis was carried out in stationary conditions, and its results were compared with those obtained through the integrated DA model to verify the KPIs of the study. The steps necessary to obtain the benchmark are detailed in the following:

1. 1) The 3D model has been defeatured, and the volume of gas contained within the cylinder walls (i.e., gas solid) necessary for the setup of the CFD analysis has been obtained by Boolean subtraction. Clearance volume values are computed through Siemens NX CAD evaluation (cf. Figure 15);

1. 2) The volume of gas has been imported into Ansys CFX software (https://www.ansys.com/it-it/products/fluids/ansys-cfx, last access on 21/11/2023);

2. 3) The inlet gas pressure was set at the inlet surface, a wall condition was imposed as a constraint to simulate the presence of the metal, and the average piston velocity was at the outlet surface to complete the boundary conditions of the model (cf. Figure 16). The valves are simulated as a porous septum;

1. 4) After the CFD run, the results have been exported in a specific MS Excel macro that correlates the different variables through the flow path (i.e., the pressure losses) to obtain the values of the flow coefficient $ {K}_s $ .

Figure 15. Volume of gas for CFD analysis and clearance volume evaluation.

Figure 16. Ansys CFX model to simulate the fluid-dynamic behavior of the cylinder.

ANN results summary

The results of the ANN for the different case studies are summarized in Figure 17, containing the configuration of the three cylinders according to each variable represented in the related boxplot with respect to the statistics of the variables of the dataset themselves (i.e., distributions, medians, quartiles, and range of data). Using boxplots to compare the results of ANN predictions with original design parameters is a powerful visual and analytical tool. It aids in assessing data distribution, detecting outliers, and above all, evaluating the consistency of the neural network’s predictions. If the boxplots of different case studies exhibit consistent patterns or variations, it provides insights into the reliability and robustness of the optimization process.

Figure 17. Boxplots summarizing ANN results.

Case study a is shown in yellow, case study b is shown in red, and case study c is represented in blue. There are overlaps of values of Var1 for cases a and b, Var6 for cases b and c, and Var8 for cases b and c (which are the discrete variables of the dataset, representing quantitative parameters).

In general, it seems that no outliers have been generated by the metamodel, with values corresponding to the different configurations of the cylinders falling in the distributions of the dataset variables. Furthermore, it emerges that the results obtained through the ANNs are independent of the geometry of the DA master model and the cylinder itself.

More specifically, and for case studies b and c in particular, it is demonstrated that even starting from a baseline configuration of a cylinder that is not included in the original dataset, the ANN delivers results regarding the single variables that are consistent with the original one in terms of distribution within the design space, although the overall topology of the flow path may vary significantly.

Comparison with CFD simulations

Having good predictability of machine performance is crucial for several reasons: it supports efficient operations, cost-effectiveness, quality assurance, customer satisfaction, and competitive advantage in industrial applications.

At the same time, assessing the design lead time of the proposed methodology applied to RC cylinders is crucial to evaluate the industrial impact of the integrated DA method, too. Design process lead time refers to the duration it takes for a design to move from the initial concept stage to completion. It’s important in industrial applications because it directly impacts time-to-market, engineering cost, and overall efficiency of the process.

The results, summarized in Table 5, are as follows:

1. a. For the first case study, the error between $ {K}_{{\mathrm{s}}_{\mathrm{ANN}}} $ obtained with the metamodel and $ {K}_{{\mathrm{s}}_{\mathrm{CFD}}} $ obtained with the CFD model is 0.1%, while the error between $ {\varepsilon}_{\mathrm{ANN}} $ obtained with the metamodel and $ {\varepsilon}_{\mathrm{CFD}} $ obtained with the CFD model is 1%, which results in an error in the estimated absorbed power of 0.3%. The design lead time to deliver the optimal configuration with the integrated method is 10 minutes vs approximately 38 hours needed to set up (8 hours), run the CFD model (25 hours with a 6 core-processor workstation able to parallelize the calculation), and export the results (5 hours).

2. b. For the second case study, the error between $ {K}_{{\mathrm{s}}_{\mathrm{ANN}}} $ obtained with the metamodel and $ {K}_{{\mathrm{s}}_{\mathrm{CFD}}} $ obtained with the CFD model is 0.3%, while the error between $ {\varepsilon}_{\mathrm{ANN}} $ obtained with the metamodel and $ {\varepsilon}_{\mathrm{CFD}} $ obtained with the CFD model is 8.7%, which results in an error in the estimated absorbed power of 1.7%. The design lead time to deliver the optimal configuration with ANNs is 10 minutes vs approximately 40 hours needed to set up (10 hours), run the CFD model (25 hours with the same workstation), and export the results (5 hours).

3. c. For the third case study, the error between $ {K}_{{\mathrm{s}}_{\mathrm{ANN}}} $ obtained with the metamodel and $ {K}_{{\mathrm{s}}_{\mathrm{CFD}}} $ obtained with the CFD model is 4.7%, while the error between $ {\varepsilon}_{\mathrm{ANN}} $ obtained with the metamodel and $ {\varepsilon}_{\mathrm{CFD}} $ obtained with the CFD model is 45%, which results in an error in the estimated absorbed power of 14.8%. The design lead time to deliver the optimal configuration with ANNs is 10 minutes vs approximately 40 hours needed to set up (10 hours), run the CFD model (25 hours with the same workstation), and export the results (5 hours).

Table 5. Results of the computational pipeline applications